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Grateful Dead

The Grateful Dead was an American rock band formed in 1965 in Palo Alto, California, known for their eclectic style that fused elements of rock, blues, jazz, folk, country, bluegrass, rock and roll, gospel, reggae, and world music with psychedelia. The band is famous for improvisation during their live performances, and attracted a devoted fan base, known as "Deadheads." According to the musician and writer Lenny Kaye, the music of the Grateful Dead "touches on ground that most other groups don't even know exists." For the range of their influences and the structure of their live performances, the Grateful Dead are considered "the pioneering godfathers of the jam band world".

The Grateful Dead was founded in the San Francisco Bay Area during the rise of the counterculture of the 1960s. The band's founding members were Jerry Garcia (lead guitar and vocals), Bob Weir (rhythm guitar and vocals), Ron "Pigpen" McKernan (keyboards, harmonica, and vocals), Phil Lesh (bass guitar and vocals), and Bill Kreutzmann (drums). Members of the Grateful Dead, originally known as the Warlocks, had played together in various Bay Area ensembles, including the traditional jug band Mother McCree's Uptown Jug Champions. Lesh was the last member to join the Warlocks before they changed their name to Grateful Dead, replacing Dana Morgan Jr., who had played bass for a few gigs. Drummer Mickey Hart and non-performing lyricist Robert Hunter joined in 1967. With the exception of McKernan, who died in 1973, and Hart, who left the band from 1971 to 1974, the core of the band stayed together for its entire 30-year history. Other official members of the band included Tom Constanten (keyboards from 1968 to 1970), John Perry Barlow (non-performing lyricist from 1971 to 1995), Keith Godchaux (keyboards and occasional vocals from 1971 to 1979), Donna Godchaux (vocals from 1972 to 1979), Brent Mydland (keyboards and vocals from 1979 to 1990), and Vince Welnick (keyboards and vocals from 1990 to 1995). Bruce Hornsby (accordion, piano, vocals) was a touring member from 1990 to 1992, as well as a guest with the band on occasion before and after the tours.

After Garcia's death in 1995, former members of the band, along with other musicians, toured as The Other Ones in 1998, 2000, and 2002, and as The Dead in 2003, 2004, and 2009. In 2015, the four surviving core members marked the band's 50th anniversary in a series of concerts in Santa Clara, Calif. and Chicago that were billed as their last performances together. There have also been several spin-offs featuring one or more core members, such as Dead & Company, Furthur, the Rhythm Devils, Phil Lesh and Friends, RatDog, and Billy & the Kids.

Despite having only one top-40 single in their 30-year career, "Touch of Grey," the Grateful Dead remained among the highest-grossing American touring acts for decades. They gained a committed fanbase by word of mouth and through the free exchange of their live recordings, encouraged by the band's allowance of taping. In 2024, they broke the record for most top-40 albums on the Billboard 200 chart. Rolling Stone named the Grateful Dead number 57 on its 2011 list of the "100 Greatest Artists of all Time". The band was inducted into the Rock and Roll Hall of Fame in 1994, and a recording of their May 8, 1977 performance at Cornell University's Barton Hall was added to the National Recording Registry of the Library of Congress in 2012.

Formation (1965–1966)
The Grateful Dead began their career as the Warlocks, a group formed in early 1965 from the remnants of a Palo Alto, California jug band called Mother McCree's Uptown Jug Champions and members of The Wildwood Boys (Jerry Garcia, Ron "Pigpen" McKernan, David Nelson, Robert Hunter, and Norm Van Maastricht). As The Wildwood Boys they played regularly at The Tangent, a folk music coffeehouse operated by Stanford Medical Center doctors Stuart "Stu" Goldstein and David "Dave" Shoenstadt on University Avenue in Palo Alto (1963). As the Warlocks, the band's first show was at Magoo's Pizza Parlor, at 639 Santa Cruz Avenue in suburban Menlo Park, on May 5, 1965, now a Harvest furniture store. The band continued playing bar shows, like Frenchy's Bikini-A-Go-Go in Hayward and, importantly, five sets a night, five nights a week, for six weeks, at the In Room  in Belmont as the Warlocks, but quickly changed the band's name after finding out that a different band known as the Warlocks had put out a record under that name. (The Velvet Underground also had to change its name from the Warlocks.)

The first show under the name Grateful Dead was in San Jose on December 4, 1965, at one of Ken Kesey's Acid Tests. Scholar Michael Kaler has written that the Dead's participation in the Acid Tests was crucial both to the development of their improvisational vocabulary and to their bonding as a band, with the group having set out to foster an intra-band musical telepathy. Kaler has further pointed out that the Dead's pursuit of a new improvisatory rock language in 1965 chronologically coincided with that same goal's adoption by Jefferson Airplane, Pink Floyd and the Velvet Underground.

Earlier demo tapes have survived, but the first of over 2,000 concerts known to have been recorded by the band's fans was a show at the Fillmore Auditorium in San Francisco on January 8, 1966. Later that month, the Grateful Dead played at the Trips Festival, a three-day psychedelic rock weekend party and event produced by Ken Kesey, Stewart Brand, and Ramon Sender, that, in conjunction with the Merry Pranksters, brought the nascent hippie movement together for the first time.

The name "Grateful Dead" was chosen from a dictionary. According to Lesh, Garcia "picked up an old Britannica World Language Dictionary ... [and] ... In that silvery elf-voice he said to me, 'Hey, man, how about the Grateful Dead?'" The definition there was "the soul of a dead person, or his angel, showing gratitude to someone who, as an act of charity, arranged their burial." According to Alan Trist, director of the Grateful Dead's music publisher company Ice Nine, Garcia found the name in the Funk & Wagnalls Folklore Dictionary, when his finger landed on that phrase while playing a game of Fictionary. In the Garcia biography Captain Trips, author Sandy Troy states that the band was smoking the psychedelic DMT at the time. The term "grateful dead" appears in folktales from a variety of cultures.

Other supporting personnel who joined early included Rock Scully, who heard of the band from Kesey and signed on as manager after meeting them at the Big Beat Acid Test; Stewart Brand, "with his side show of taped music and slides of Indian life, a multimedia presentation" at the Big Beat and then, expanded, at the Trips Festival; and Owsley Stanley, the "Acid King" whose LSD supplied the Acid Tests and who, in early 1966, became the band's financial backer, renting them a house on the fringes of Watts, Los Angeles, and buying them sound equipment. "We were living solely off of Owsley's good graces at that time. ... [His] trip was he wanted to design equipment for us, and we were going to have to be in sort of a lab situation for him to do it", said Garcia.

Pigpen era (1967–1972)
One of the group's earliest major performances in 1967 was the Mantra-Rock Dance, a musical event held on January 29, 1967, at the Avalon Ballroom by the San Francisco Hare Krishna temple. The Grateful Dead performed at the event along with the Hare Krishna founder Bhaktivedanta Swami, poet Allen Ginsberg, bands Moby Grape and Big Brother and the Holding Company with Janis Joplin, donating proceeds to the temple. The band's first LP, The Grateful Dead, was released on Warner Brothers in 1967.

On May 3, 1968, the band played a free concert at Columbia University during the anti–Vietnam War student protests during which students occupied several campus buildings. In order to play, the band, equipment and all, had to be “smuggled” on campus in the back of a bread delivery truck. “We were already jamming away before the security and police could stop us.”

Classically trained trumpeter Phil Lesh performed on bass guitar. Bob Weir, the youngest original member of the group, played rhythm guitar. Ron "Pigpen" McKernan played keyboards, percussion, and harmonica until shortly before his death in 1973 at the age of 27. Garcia, Weir, and McKernan shared the lead vocal duties more or less equally; Lesh sang only a few leads, but his tenor was a key part of the band's three-part vocal harmonies. Bill Kreutzmann played drums, and in September 1967 was joined by a second drummer, New York City native Mickey Hart, who also played a wide variety of other percussion instruments.

1970 included tour dates in New Orleans, where the band performed at The Warehouse for two nights. On January 31, 1970, the local police raided their hotel on Bourbon Street and arrested and charged 19 people with possession of various drugs. The second night's concert was performed as scheduled after bail was posted. Eventually, the charges were dismissed, except those against sound engineer Owsley Stanley, who was already facing charges in California for manufacturing LSD. This event was later memorialized in the lyrics of “Truckin'", a single from American Beauty that reached number 64 on the charts.

Hart took time off from the band in February 1971, after his father, an accountant, absconded with much of the band's money; Kreutzmann was once again as the sole percussionist. Hart rejoined the Grateful Dead for good in October 1974. Tom "TC" Constanten was added as a second keyboardist from 1968 to 1970, to help Pigpen keep up with an increasingly psychedelic sound, while Pigpen transitioned into playing various percussion instruments and vocals.

After Constanten's departure, Pigpen reclaimed his position as sole keyboardist. Less than two years later, in late 1971, Pigpen was joined by another keyboardist, Keith Godchaux, who played grand piano alongside Pigpen's Hammond B-3 organ. In early 1972, Keith's wife, Donna Jean Godchaux, joined the Grateful Dead as a backing vocalist.

Following the Grateful Dead's "Europe '72" tour, Pigpen's health had deteriorated to the point that he could no longer tour with the band. His final concert appearance was June 17, 1972, at the Hollywood Bowl, in Los Angeles; he died on March 8, 1973, of complications from liver damage.

Godchaux era (1972–1979)
Pigpen's death did not slow down the Grateful Dead. With the help of manager Ron Rakow, the band soon formed its own record label, Grateful Dead Records. Later that year, it released its next studio album, the jazz-influenced Wake of the Flood, which became their biggest commercial success thus far. Meanwhile, capitalizing on the album's success, the band soon went back to the studio, and in June 1974 released another album, From the Mars Hotel. Not long after, the Dead decided to take a hiatus from live touring. The band performed a series of five concerts at the Winterland Ballroom in San Francisco in October 1974, and delved into various other projects. The Winterland concerts were filmed, and Garcia compiled the footage into The Grateful Dead Movie, a feature-length concert film released in 1977.

In September 1975, the Dead released their eighth studio album, Blues for Allah. The band resumed touring in June 1976, playing multiple dates in small theaters, rather than the stadium shows that had become common, and had exhausted them, in 1974. That same year, they signed with Arista Records, and the new contract produced Terrapin Station in July 1977. The band's tour in the spring of that year is held in high regard by its fans, and its concert of May 8 at Cornell University is often considered one of the best performances of its career. Their September 1977 concert at Raceway Park in Old Bridge Township, New Jersey was attended by 107,019 people and held the record for largest-ticketed concert in the United States by a single act for 47 years.

Keith and Donna Jean Godchaux left the band in February 1979, citing artistic differences.

Mydland/Welnick era (1979–1995)
Following the Godchauxs' departure, Brent Mydland joined as keyboardist and vocalist and was considered "the perfect fit." The Godchauxs then formed the Heart of Gold Band, before Keith died in a car accident in July 1980. Mydland was the keyboardist for the Grateful Dead for 11 years until his death by narcotics overdose in July 1990, becoming the third keyboardist to die.

Shortly after Mydland found his place in the early 1980s, Garcia's health began to decline. He became a frequent smoker of "Persian," a type of heroin, and he gained weight at a rapid pace. He lost his liveliness on stage, his voice was strained, and Deadheads worried for his health. After he began to curtail his opiate usage gradually in 1985, Garcia slipped into a diabetic coma for several days in July 1986, leading to the cancelation of all concerts in the fall of that year. Garcia recovered, the band released In the Dark in July 1987, which became its best-selling studio album and produced its only top-40 single, "Touch of Grey," Also, that year, the group toured with Bob Dylan, as heard on the album Dylan & the Dead.

Mydland died in July 1990 and Vince Welnick, former keyboardist for the Tubes, joined as a band member, while Bruce Hornsby, who had a successful career with his band the Range, joined temporarily as a bridge to help Welnick learn songs. Both performed on keyboards and vocals—Welnick until the band's end, and Hornsby mainly from 1990 to 1992.

Saxophonist Branford Marsalis played five concerts with the band between 1990 and 1994.

The Grateful Dead performed its final concert on July 9, 1995, at Soldier Field in Chicago.

Aftermath (1995–present)
Jerry Garcia died on August 9, 1995. A few months after Garcia's death, the remaining members of the Grateful Dead decided to disband. Since that time, there have been a number of reunions by the surviving members involving various combinations of musicians. Additionally, the former members have also begun or continued individual projects.

In 1998, Bob Weir, Phil Lesh, and Mickey Hart, along with several other musicians, formed a band called the Other Ones, and performed a number of concerts that year, releasing a live album, The Strange Remain, the following year. In 2000, the Other Ones toured again, this time with Kreutzmann but without Lesh. After taking another year off, the band toured again in 2002 with Lesh. That year, the Other Ones then included all four living former Grateful Dead members who had been in the band for most or all of its history. At different times the shifting lineup of the Other Ones also included guitarists Mark Karan, Steve Kimock, and Jimmy Herring, keyboardists Bruce Hornsby, Jeff Chimenti, and Rob Barraco, saxophonist Dave Ellis, drummer John Molo, bassist Alphonso Johnson, and vocalist Susan Tedeschi.

In 2003, the Other Ones, still including Weir, Lesh, Hart, and Kreutzmann, changed their name to the Dead. The Dead toured the United States in 2003, 2004 and 2009. The band's lineups included Jimmy Herring and Warren Haynes on guitar, Jeff Chimenti and Rob Barraco on keyboards, and Joan Osborne on vocals. In 2008, members of the Dead played two concerts, called "Deadheads for Obama" and "Change Rocks".

Following the 2009 Dead tour, Lesh and Weir formed the band Furthur, which debuted in September 2009. Joining Lesh and Weir in Furthur were John Kadlecik (guitar), Jeff Chimenti (keyboards), Joe Russo (drums), Jay Lane (drums), Sunshine Becker (vocals), and Zoe Ellis (vocals). Lane and Ellis left the band in 2010, and vocalist Jeff Pehrson joined later that year. Furthur disbanded in 2014.

In 2010, Hart and Kreutzmann re-formed the Rhythm Devils, and played a summer concert tour.

Since 1995, the former members of the Grateful Dead have also pursued solo music careers. Both Bob Weir & RatDog and Phil Lesh and Friends  have performed many concerts and released several albums. Mickey Hart and Bill Kreutzmann have also each released a few albums. Hart has toured with his world music percussion ensemble Planet Drum as well as the Mickey Hart Band. Kreutzmann has led several different bands, including BK3, 7 Walkers (with Papa Mali), and Billy & the Kids. Donna Godchaux has returned to the music scene, with the Donna Jean Godchaux Band, and Tom Constanten also continues to write and perform music. All of these groups continue to play Grateful Dead music.

In October 2014, it was announced that Martin Scorsese would produce a documentary film about the Grateful Dead, to be directed by Amir Bar-Lev. David Lemieux supervised the musical selection, and Weir, Hart, Kreutzmann, and Lesh agreed to new interviews for the film. Bar-Lev's four-hour documentary, titled Long Strange Trip, was released in 2017.

"Fare Thee Well"
In 2015, Weir, Lesh, Kreutzmann, and Hart reunited for five concerts called "Fare Thee Well: Celebrating 50 Years of the Grateful Dead". The shows were performed on June 27 and 28 at Levi's Stadium in Santa Clara, California, and on July 3, 4 and 5 at Soldier Field in Chicago. The band stated that this would be the final time that Weir, Lesh, Hart, and Kreutzmann would perform together. They were joined by Trey Anastasio of Phish on guitar, Jeff Chimenti on keyboards, and Bruce Hornsby on piano. Demand for tickets was very high. The concerts were simulcast via various media. The Chicago shows have been released as a box set of CDs and DVDs.

Dead & Company
In the fall of 2015, Mickey Hart, Bill Kreutzmann and Bob Weir joined with guitarist John Mayer, keyboardist Jeff Chimenti, and bassist Oteil Burbridge to tour in a band called Dead & Company. Mayer recounts that in 2011 he was listening to Pandora and happened upon the Grateful Dead song "Althea", and that soon Grateful Dead music was all he would listen to. The band played six tours: October–December 2015, June–July 2016, May–July 2017., May–August 2018, and May–July 2019. On October–November 2019 they played 6 dates on the "2019 Fall Fun Run". On December 27 and 28, they played at The Forum in Inglewood (Los Angeles), California as part of their "2019 New Year's Run" tour. On December 30 and 31, they played in their hometown of San Francisco at the Chase Center, featuring a bi-plane that descended from the ceiling of the Chase Center carrying the daughters of Jerry Garcia, Trixie Garcia and her half-sister, Ken Kesey's daughter Sunshine Kesey, dropping rose petals on the audience as they toured the arena.

Barlow died in 2018 and Hunter in 2019.

In 2022, John Mayer announced that Dead & Company's summer 2023 tour will be their last.

Musical style and legacy
The Grateful Dead formed during the era when bands such as the Beatles, the Beach Boys and the Rolling Stones were dominating the airwaves. "The Beatles were why we turned from a jug band into a rock 'n' roll band", said Bob Weir. "What we saw them doing was impossibly attractive. I couldn't think of anything else more worth doing." Former folk-scene star Bob Dylan had recently put out a couple of records featuring electric instrumentation. Grateful Dead members have said that it was after attending a concert by the touring New York City band the Lovin' Spoonful that they decided to "go electric" and look for a "dirtier" sound. Jerry Garcia and Bob Weir (both of whom had been immersed in the American folk music revival of the late 1950s and early 1960s), were open-minded about the use of electric guitars.

The Grateful Dead's early music (in the mid-1960s) was part of the process of establishing what "psychedelic music" was, but theirs was essentially a "street party" form of it. They developed their "psychedelic" playing as a result of meeting Ken Kesey in Palo Alto, California, and subsequently becoming the house band for the Acid Tests he staged. They did not fit their music to an established category such as pop rock, blues, folk rock, or country & western. Individual tunes within their repertoire could be identified under one of these stylistic labels, but overall their music drew on all of these genres and, more frequently, melded several of them. Bill Graham said of the Grateful Dead, "They're not the best at what they do, they're the only ones that do what they do." Academics Paul Hegarty and Martin Halliwell argued that the Grateful Dead were "not merely as precursors of prog but as essential developments of progressiveness in its early days". Often (both in performance and on recording) the Dead left room for exploratory, spacey soundscapes.

Their live shows, fed by an improvisational approach to music, were different from most touring bands. While rock and roll bands often rehearse a standard set, played with minor variations, the Grateful Dead did not prepare in this way. Garcia stated in a 1966 interview, "We don't make up our sets beforehand. We'd rather work off the tops of our heads than off a piece of paper." They maintained this approach throughout their career. For each performance, the band drew material from an active list of a hundred or so songs.

The 1969 live album Live/Dead did capture the band in-form, but commercial success did not come until Workingman's Dead and American Beauty, both released in 1970. These records largely featured the band's laid-back acoustic musicianship and more traditional song structures. With their rootsy, eclectic stylings, particularly evident on the latter two albums, the band pioneered the hybrid Americana genre.

Beginning in the early 1990s, a new generation of bands became inspired by the Grateful Dead's improvisational ethos and marketing strategy, and began to incorporate elements of the Grateful Dead's live performances into their own shows. These include the nightly alteration of setlists, frequent improvisation, the blending of genres, and the allowance of taping, which would often contribute to the development of a dedicated fanbase. Bands associated with the expansion of the "jam scene" include Phish, The String Cheese Incident, Widespread Panic, Blues Traveler, moe., and the Disco Biscuits. Many of these groups began to look past the American roots music that the Grateful Dead drew inspiration from, and incorporated elements of progressive rock, hard rock, and electronica. At the same time, the Internet gained popularity and provided a medium for fans to discuss these bands and their performances and download MP3s. The Grateful Dead, as well as Phish, were one of the first bands to have a Usenet newsgroup.

Musicianship
As the band and its sound matured over thirty years of touring, playing, and recording, each member's stylistic contribution became more defined, consistent, and identifiable. Garcia's lead lines were fluid, supple and spare, owing a great deal of their character to his experience playing Scruggs style banjo, an approach which often makes use of note syncopation, accenting, arpeggios, staccato chromatic runs, and the anticipation of the downbeat.

Garcia had a distinctive sense of timing, often weaving in and out of the groove established by the rest of the band as if he were pushing the beat. His lead lines were also immensely influenced by jazz soloists: Garcia cited Miles Davis, Ornette Coleman, Bill Evans, Pat Martino, George Benson, Al Di Meola, Art Tatum, Duke Ellington, and Django Reinhardt as primary influences, and frequently utilized techniques common to country and blues music in songs that called back to those traditions.

Garcia often switched scales in the midst of a solo depending upon the chord changes played underneath, though he nearly always finished phrases by landing on the chord-tones. Jerry most frequently played in the Mixolydian mode, though his solos and phrases often incorporated notes from the Dorian and major/minor pentatonic scales. Particularly in the late 1960s, Garcia occasionally incorporated melodic lines derived from Indian ragas into the band's extended, psychedelic improvisation, likely inspired by John Coltrane and other jazz artists' interest in the sitar music of Ravi Shankar.

Lesh was originally a classically trained trumpet player with an extensive background in music theory, but did not tend to play traditional blues-based bass forms. He often played more melodic, symphonic and complex lines, often sounding like a second lead guitar. In contrast to most bassists in popular music, Lesh often avoids playing the root of a chord on the downbeat, instead withholding as a means to build tension. Lesh also rarely repeats the same bassline, even from performance to performance of the same song, and often plays off of or around the other instruments with a syncopated, staccato bounce that contributes to the Dead's unique rhythmic character.

Weir, too, was not a traditional rhythm guitarist, but tended to play unique inversions at the upper end of the Dead's sound. Weir modeled his style of playing after jazz pianist McCoy Tyner and attempted to replicate the interplay between John Coltrane and Tyner in his support, and occasional subversion, of the harmonic structure of Garcia's voice leadings. This would often influence the direction the band's improvisation would take on a given night. Weir and Garcia's respective positions as rhythm and lead guitarist were not always strictly adhered to, as Weir would often incorporate short melodic phrases into his playing to support Garcia and occasionally took solos, often played with a slide. Weir's playing is characterized by a "spiky, staccato" sound.

The band's two drummers, Mickey Hart and Bill Kreutzmann, developed a unique, complex interplay, balancing Kreutzmann's steady shuffle beat with Hart's interest in percussion styles outside the rock tradition. Kreuzmann has said, "I like to establish a feeling and then add radical or oblique juxtapositions to that feeling." Hart incorporated an 11-count measure to his drumming, bringing a dimension to the band's sound that became an important part of its style. He had studied tabla drumming and incorporated rhythms and instruments from world music, and later electronic music, into the band's live performances.

The Dead's live performances featured multiple types of improvisation derived from a vast array of musical traditions. Not unlike many rock bands of their time, the majority of the Dead's songs feature a designated section in which an instrumental break occurs over the chord changes. These sections typically feature solos by Garcia that often originate as variations on the song's melody, but go on to create dynamic phrases that resolve by returning to the chord-tones. Not unlike traditional improvisational jazz, they may occasionally feature several solos by multiple instruments within an undecided number of bars, such as a keyboardist, before returning to the melody. At the same time, Dead shows almost always feature a more collective, modal approach to improvisation that typically occurs during segues between songs before the band modulates to a new tonal center. Some of the Dead's more extended jam vehicles, such as "The Other One", "Dark Star", and "Playing in the Band" almost exclusively make use of modulation between modes to accompany simple two-chord progressions.

Lyrical themes
Following the songwriting renaissance that defined the band's early 1970s period, as reflected in the albums Workingman's Dead and American Beauty, Robert Hunter, Jerry Garcia's primary lyrical partner, frequently made use of motifs common to American folklore including trains, guns, elements, traditional musical instruments, gambling, murder, animals, alcohol, descriptions of American geography, and religious symbolism to illustrate themes involving love and loss, life and death, beauty and horror, and chaos and order. Following in the footsteps of several American musical traditions, these songs are often confessional and feature narration from the perspective of an antihero. Critic Robert Christgau described them as "American myths" that later gave way to "the old karma-go-round".

An extremely common feature in both Robert Hunter's lyrics, as well as the band's visual iconography, is the presence of dualistic and opposing imagery illustrating the dynamic range of the human experience (Heaven and hell, law and crime, dark and light, etc.). Hunter and Garcia's earlier, more directly psychedelic-influenced compositions often make use of surreal imagery, nonsense, and whimsey reflective of traditions in English poetry. In a retrospective, The New Yorker described Hunter's verses as "elliptical, by turns vivid and gnomic", which were often "hippie poetry about roses and bells and dew". Grateful Dead biographer Dennis McNally has described Hunter's lyrics as creating "a non-literal hyper-Americana" weaving a psychedelic, kaleidoscopic tapestry in the hopes of elucidating America's national character. At least one of Hunter and Bob Weir's collaborations, "Jack Straw", was inspired by the work of John Steinbeck.

Merchandising and representation
Hal Kant was an entertainment industry attorney who specialized in representing musical groups. He spent 35 years as principal lawyer and general counsel for the Grateful Dead, a position in the group that was so strong that his business cards with the band identified his role as "Czar".

Kant brought the band millions of dollars in revenue through his management of the band's intellectual property and merchandising rights. At Kant's recommendation, the group was one of the few rock 'n roll pioneers to retain ownership of their music masters and publishing rights.

In 2006, the Grateful Dead signed a ten-year licensing agreement with Rhino Entertainment to manage the band's business interests including the release of musical recordings, merchandising, and marketing. The band retained creative control and kept ownership of its music catalog.

A Grateful Dead video game titled Grateful Dead Game – The Epic Tour was released in April 2012 and was created by Curious Sense.

In November 2022, the children's book The ABCs of The Grateful Dead was released. Authorized by the group, it was written by Howie Abrams, illustrated by Michael "Kaves" McLeer, and published by Simon & Schuster.

Sponsorship of 1992 Lithuanian Olympic Basketball Team
After Lithuania gained its independence from the USSR, the country announced its withdrawal from the 1992 Olympics due to the lack of any money to sponsor participants. But NBA star Šarūnas Marčiulionis, a native Lithuanian basketball star, wanted to help his native team to compete. His efforts resulted in a call from representatives of the Grateful Dead who set up a meeting with the band members. The band agreed to fund transportation costs for the team (about five thousand dollars) along with Grateful Dead designs for the team's jerseys and shorts. The Lithuanian basketball team won the bronze medal and the Lithuanian basketball/Grateful Dead T-shirts became part of pop culture, especially in Lithuania. The incident was covered by the documentary The Other Dream Team.

Live performances
The Grateful Dead toured constantly throughout their career, playing more than 2,300 concerts. They promoted a sense of community among their fans, who became known as "Deadheads", many of whom followed their tours for months or years on end. Around concert venues, an impromptu communal marketplace known as 'Shakedown Street' was created by Deadheads to serve as centers of activity where fans could buy and sell anything from grilled cheese sandwiches to home-made t-shirts and recordings of Grateful Dead concerts.

In their early career, the band also dedicated their time and talents to their community, the Haight-Ashbury area of San Francisco, making available free food, lodging, music, and health care to all. It has been said that the band performed "more free concerts than any band in the history of music".

With the exception of 1975, when the band was on hiatus and played only four concerts, Grateful Dead performed many concerts every year, from their formation in April 1965, until July 9, 1995. Initially all their shows were in California, principally in the San Francisco Bay Area and in or near Los Angeles. They also performed, in 1965 and 1966, with Ken Kesey and the Merry Pranksters, as the house band for the Acid Tests.

In 1967, they toured nationally, including their first performance in New York City. They appeared at the Monterey Pop Festival in 1967, the Woodstock Festival in 1969 and the Festival Express train tour across Canada in 1970. They were scheduled to appear as the final act at the infamous Altamont Free Concert on December 6, 1969, after the Rolling Stones but withdrew after security concerns. "That's the way things went at Altamont—so badly that the Grateful Dead, prime organizers and movers of the festival, didn't even get to play", staff at Rolling Stone magazine wrote in a detailed narrative on the event.

Their first UK performance was at the Hollywood Music Festival in 1970. Their largest concert audience came in 1973 when they played, along with the Allman Brothers Band and the Band, before an estimated 600,000 people at the Summer Jam at Watkins Glen. They played to an estimated total of 25 million people, more than any other band, with audiences of up to 80,000 attending a single show. Many of these concerts were preserved in the band's tape vault, and several dozen have since been released on CD and as downloads. The Dead were known for the tremendous variation in their setlists from night to night—the list of songs documented to have been played by the band exceeds 500. The band has released four concert videos under the name View from the Vault. In 1978, they played three nights at the Great Pyramid of Giza in Egypt.

In the 1990s, the Grateful Dead earned a total of $285 million in revenue from their concert tours, the second-highest during the 1990s, with the Rolling Stones earning the most. This figure is representative of tour revenue through 1995, as touring stopped after the death of Jerry Garcia.

In a 1991 PBS documentary, segment host Buck Henry attended an August 1991 concert at Shoreline Amphitheatre and gleaned some information from some band members about the Grateful Dead phenomenon and its success. At the time, Jerry Garcia stated, "We didn't really invent the Grateful Dead, the crowd invented the Grateful Dead, you know what I mean? We were sort of standing in line, and uh, it's gone way past our expectations, way past, so it's, we've been going along with it to see what it's gonna do next." Mickey Hart said, "This is one of the last places in America that you can really have this kind of fun, you know, considering the political climate and so forth." Hart also stated that "the transformative power of the Grateful Dead is really the essence of it; it's what it can do to your consciousness. We're more into transportation than we are into music, per se, I mean, the business of the Grateful Dead is transportation." One of the band's largest concerts took place just months before Garcia's death — at their outdoor show with Bob Dylan in Highgate, Vermont, on June 15, 1995. The crowd was estimated to be over 90,000; overnight camping was allowed and about a third of the audience got in without having purchased a ticket.

Their numerous studio albums were generally collections of new songs that they had first played in concert. The band was also famous for its extended musical improvisations, having been described as having never played the same song the same way twice. Their concert sets often blended songs, one into the next, often for more than three songs at a time.

Concert sound systems
The Wall of Sound was a large sound system designed specifically for the band. The band was never satisfied with the house system anywhere they played. After the Monterey Pop Festival, the band's crew 'borrowed' some of the other performers' sound equipment and used it to host some free shows in San Francisco. In their early days, soundman Owsley "Bear" Stanley designed a public address (PA) and monitor system for them. Stanley was the Grateful Dead's soundman for many years; he was also one of the largest suppliers of LSD.

Stanley's sound systems were delicate and finicky, and frequently brought shows to a halt with technical breakdowns. After Stanley went to jail for manufacturing LSD in 1970, the group briefly used house PAs, but found them to be even less reliable than those built by their former soundman. On February 2, 1970, the group contacted Bob Heil to use his system. In 1971, the band purchased their first solid-state sound system from Alembic Studios. Because of this, Alembic would play an integral role in the research, development, and production of the Wall of Sound. The band also welcomed Dan Healy into the fold on a permanent basis that year. Healy would mix the Grateful Dead's live sound until 1993.

Following Jerry Garcia's death and the band's breakup in 1995, their current sound system was inherited by Dave Matthews Band. Dave Matthews Band debuted the sound system April 30, 1996, at the first show of their 1996 tour in Richmond, Virginia.

Tapes
Like several other bands at the time, the Grateful Dead allowed their fans to record their shows. For many years the tapers set up their microphones wherever they could, and the eventual forest of microphones became a problem for the sound crew. Eventually, this was solved by having a dedicated taping section located behind the soundboard, which required a special "tapers" ticket. The band allowed sharing of their shows, as long as no profits were made on the sale of the tapes.

Of the approximately 2,350 shows the Grateful Dead played, almost 2,200 were taped, and most of these are available online. The band began collecting and cataloging tapes early on and Dick Latvala was their keeper. "Dick's Picks" is named after Latvala. After his death in 1999, David Lemieux gradually took the post. Concert set lists from a subset of 1,590 Grateful Dead shows were used to perform a comparative analysis between how songs were played in concert and how they are listened online by Last.fm members. In their book Marketing Lessons from the Grateful Dead: What Every Business Can Learn From the Most Iconic Band in History, David Meerman Scott and Brian Halligan identify the taper section as a crucial contributor to increasing the Grateful Dead's fan base.

Iconography
Over the years, a number of iconic images have come to be associated with the Grateful Dead. Many of these images originated as artwork for concert posters or album covers.

 * Skull and Roses
 * The skull and roses design was composed by Alton Kelley and Stanley Mouse, who added lettering and color, respectively, to a black and white drawing by Edmund Joseph Sullivan. Sullivan's drawing was an illustration for a 1913 edition of the Rubaiyat of Omar Khayyam. Earlier antecedents include the custom of exhibiting the relic skulls of Christian martyrs decorated with roses on their feast days. The rose is an attribute of Saint Valentine, who according to one legend, was martyred by decapitation. Accordingly, in Rome, at the church dedicated to him, the observance of his feast day included the display of his skull surrounded by roses. Kelley and Mouse's design originally appeared on a poster for the September 16 and 17, 1966, Dead shows at the Avalon Ballroom. Later, it was used as the cover for the album Grateful Dead (1971). The album is sometimes referred to as Skull and Roses.

 * Jester
 * Another icon of the Dead is a skeleton dressed as a jester and holding a lute. This image was an airbrush painting, created by Stanley Mouse in 1972. It was originally used for the cover of The Grateful Dead Songbook.

 * "Dancing" Bears
 * A series of stylized bears who appear to be dancing was drawn by Bob Thomas as part of the back cover for the album History of the Grateful Dead, Volume One (Bear's Choice) (1973). Thomas reported that he based the bears on a lead sort from an unknown font. The bear is a reference to Owsley "Bear" Stanley, who recorded and produced the album. Bear himself wrote, "the bears on the album cover are not really 'dancing'. I don't know why people think they are; their positions are quite obviously those of a high-stepping march."

 * Steal Your Face Skull
 * Perhaps the best-known Grateful Dead art icon is a red, white, and blue skull with a lightning bolt through it. The lightning bolt skull can be found on the cover of the album Steal Your Face (1976), and the image is sometimes known by that name. It was designed by Owsley Stanley and artist Bob Thomas, and was originally used as a logo to mark the band's equipment.

 * Dancing Terrapins
 * The two dancing terrapins first appeared on the cover of the album Terrapin Station (1977). They were drawn by Kelley and Mouse, based on a drawing by Heinrich Kley. Since then these turtles have become one of the Grateful Dead's most recognizable logos.

 * Uncle Sam Skeleton
 * The Uncle Sam skeleton was devised by Gary Gutierrez as part of the animation for The Grateful Dead Movie (1977). The image combines the Grateful Dead skeleton motif with the character of Uncle Sam, a reference to the then-recently written song "U.S. Blues", which plays during the animation.

Deadheads
Fans and enthusiasts of the band are commonly referred to as Deadheads. While the origin of the term may be unclear, Dead Heads were made canon by the notice placed inside the Skull and Roses (1971) album by manager Jon McIntire:

"DEAD FREAKS UNITE: Who are you? Where are you? How are you? Send us your name and address and we'll keep you informed. Dead Heads, P.O. Box 1065, San Rafael, California 94901." As each show featured a new setlist and a great deal of improvisation, Deadheads would often follow the band from city to city, attending many shows on a given tour. Many Deadheads speak of being drawn to the culture due to the sense of community that the band's shows tended to foster. Though Deadheads came from a wide array of demographics, many attempted to reproduce the aesthetics and values of the 1960s counterculture and were often stigmatized in the media. Because of the stereotyping of Deadheads as hippies, the band's shows became a common target for officials in the DEA and arrests at shows became common.

As a group, the Deadheads were considered very mellow. "I'd rather work nine Grateful Dead concerts than one Oregon football game," Police Det. Rick Raynor said. "They don't get belligerent like they do at the games." Despite this reputation, in the mid-1990s, as the band's popularity grew, there were a series of minor scuffles occurring at shows that peaked with a large scale riot at the Deer Creek Music Center near Indianapolis in July 1995. This gate crashing incident caused the band to cancel the following night's show. Deadheads who appeared on the scene after the band's 1987 hit single "Touch of Grey", were often disparagingly referred to by older fans as "Touchheads". Beginning in the 1980s, a number of definable sects of Deadheads began to appear on the scene. These included the Wharf Rats, as well as the "spinners", named for whirling-style of dancing and their use of the band's music to facilitate mystical experiences.

Deadheads, particularly those who collected tapes, were known for keeping close records of the band's setlists and for comparing various live versions of the band's songs, as reflected in publications such as the various editions of "Deadbase" and "The Deadhead's Taping Compendium". This practice continues into the 21st century on digital forums and websites such as the Internet Archive, which features live recordings of nearly every available Grateful Dead show and allows users to discuss and review the site's shows.

The band has a number of influential and celebrity fans, including politicians, businesspeople, journalists, and other musicians.

Donation of archives to UC Santa Cruz
On April 24, 2008, members Bob Weir and Mickey Hart, along with Nion McEvoy, CEO of Chronicle Books, UC Santa Cruz chancellor George Blumenthal, and UC Santa Cruz librarian Virginia Steel, held a press conference announcing UCSC's McHenry Library would be the permanent home of the Grateful Dead Archive, which includes a complete archival history from 1965 to the present. The archive includes correspondence, photographs, fliers, posters, and several other forms of memorabilia and records of the band. Also included are unreleased videos of interviews and TV appearances that will be installed for visitors to view, as well as stage backdrops and other props from the band's concerts.

Blumenthal stated at the event, "The Grateful Dead Archive represents one of the most significant popular cultural collections of the 20th century; UC Santa Cruz is honored to receive this invaluable gift. The Grateful Dead and UC Santa Cruz are both highly innovative institutions—born the same year—that continue to make a major, positive impact on the world." Guitarist Bob Weir stated "We looked around, and UC Santa Cruz seems the best possible home. If you ever wrote the Grateful Dead a letter, you'll probably find it there!"

Professor of music Fredric Lieberman was the key contact between the band and the university, who let the university know about the search for a home for the archive, and who had collaborated with Mickey Hart on three books in the past, Planet Drum (1990), Drumming at the Edge of Magic (1991), and Spirit into Sound (2006).

The first large-scale exhibition of materials from the Grateful Dead Archive was mounted at the New-York Historical Society in 2010.

Awards
In 2004, Rolling Stone ranked the Grateful Dead No. 57 on their list of the 100 Greatest Artists of All Time.

On February 10, 2007, the Grateful Dead received a Grammy Lifetime Achievement Award. The award was accepted on behalf of the band by Mickey Hart and Bill Kreutzmann.

In 2011, a recording of the Grateful Dead's May 8, 1977, concert at Cornell University's Barton Hall was selected for induction into the National Recording Registry of the Library of Congress.

Twelve members of the Grateful Dead (the eleven official performing members plus Robert Hunter) were inducted into the Rock and Roll Hall of Fame in 1994, and Bruce Hornsby was their presenter.

Members
Lead guitarist Jerry Garcia was often viewed both by the public and the media as the leader or primary spokesperson for the Grateful Dead, but was reluctant to be perceived that way, especially since he and the other group members saw themselves as equal participants and contributors to their collective musical and creative output. Garcia, a native of San Francisco, grew up in the Excelsior District. One of his main influences was bluegrass music, and he also performed—on banjo, one of his other great instrumental loves, along with the pedal steel guitar—in bluegrass bands, notably Old & In the Way with mandolinist David Grisman.

Ned Lagin, a young MIT student and friend of the band, guested with them many times from 1970 through 1975, providing a second keyboard as well as synthesizers. Upon graduating from MIT, he began touring with the band fulltime in 1974, performing sets of electronic music with Phil Lesh, occasionally with Garcia and Kreutzmann, during the band's intermission. The "Ned and Phil" set became a regular fixture of that era, and was featured nearly every night during their Summer '74 and Europe '74 tours, as well as their five-night residency at the Winterland Ballroom during October 1974. Lagin is also featured in The Grateful Dead Movie. During 1974 and 1975, he would also occasionally play entire sets with the band, usually on Garcia's side of the stage, before ending his touring relationship with the band and focusing on his solo music projects, such as his album Seastones, which features several members of the Dead.

Bruce Hornsby never officially joined the band full-time because of his other commitments, but he did play keyboards at most Dead shows between September 1990 and March 1992, and sat in with the band over 100 times in all between 1988 and 1995. He added several Dead songs to his own live shows and Jerry Garcia referred to him as a "floating member" who could come and go as he pleased.

Robert Hunter and John Perry Barlow were the band's primary lyricists, starting in 1967 and 1971, respectively, and continuing until the band's dissolution. Hunter collaborated mostly with Garcia and Barlow mostly with Weir, though each wrote with other band members as well. Both are listed as official members at Dead.net, the band's website, alongside the performing members. Barlow was the only member not inducted into the Rock and Roll Hall of Fame.

Discography

 * The Grateful Dead (1967)
 * Anthem of the Sun (1968)
 * Aoxomoxoa (1969)
 * Live/Dead (1969)
 * Workingman's Dead (1970)
 * American Beauty (1970)
 * Grateful Dead (Skull & Roses) (1971)
 * Europe '72 (1972)
 * History of the Grateful Dead, Volume One (Bear's Choice) (1973)
 * Wake of the Flood (1973)
 * From the Mars Hotel (1974)
 * Blues for Allah (1975)
 * Steal Your Face (1976)
 * Terrapin Station (1977)
 * Shakedown Street (1978)
 * Go to Heaven (1980)
 * Reckoning (1981)
 * Dead Set (1981)
 * In the Dark (1987)
 * Dylan & the Dead (1989)
 * Built to Last (1989)
 * Without a Net (1990)

title: Grateful Dead


text:
Groupoid

In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a:
 * Group with a partial function replacing the binary operation;
 * Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation on the morphisms, called inverse by analogy with group theory. A groupoid where there is only one object is a usual group.

In the presence of dependent typing, a category in general can be viewed as a typed monoid, and similarly, a groupoid can be viewed as simply a typed group. The morphisms take one from one object to another, and form a dependent family of types, thus morphisms might be typed $$g:A \rightarrow B$$, $$h:B \rightarrow C$$, say. Composition is then a total function: $$\circ : (B \rightarrow C) \rightarrow (A \rightarrow B) \rightarrow A \rightarrow C $$, so that $$h \circ g : A \rightarrow C $$.

Special cases include:
 * Setoids: sets that come with an equivalence relation,
 * G-sets: sets equipped with an action of a group $$G$$.

Groupoids are often used to reason about geometrical objects such as manifolds. introduced groupoids implicitly via Brandt semigroups.

Algebraic
A groupoid can be viewed as an algebraic structure consisting of a set with a binary partial function. Precisely, it is a non-empty set $$G$$ with a unary operation $${}^{-1}:G\to G,$$ and a partial function $$*:G\times G \rightharpoonup G$$. Here * is not a binary operation because it is not necessarily defined for all pairs of elements of $$G$$. The precise conditions under which $$*$$ is defined are not articulated here and vary by situation.

The operations $$\ast$$ and −1 have the following axiomatic properties: For all $$a$$, $$b$$, and $$c$$ in $$G$$,
 * 1) Associativity: If $$a*b$$ and $$b*c$$ are defined, then $$(a * b) * c$$ and $$a * (b * c)$$ are defined and are equal.  Conversely, if one of $$(a * b) * c$$ or $$a * (b * c)$$ is defined, then they are both defined (and they are equal to each other), and $$a*b$$ and $$b*c$$ are also defined.
 * 2) Inverse: $$a^{-1} * a$$ and $$a*{a^{-1}}$$ are always defined.
 * 3) Identity: If $$a*b$$ is defined, then $$a*b*{b^{-1}} = a$$, and $${a^{-1}} * a * b = b$$.  (The previous two axioms already show that these expressions are defined and unambiguous.)

Two easy and convenient properties follow from these axioms:
 * $$(a^{-1})^{-1} = a$$,
 * If $$a*b$$ is defined, then $$(a*b)^{-1} = b^{-1} * a^{-1}$$.

Category theoretic
A groupoid is a small category in which every morphism is an isomorphism, i.e., invertible. More explicitly, a groupoid G is a set G0 of objects with
 * for each pair of objects x and y a (possibly empty) set G(x,y) of morphisms (or arrows) from x to y; we write f : x → y to indicate that f is an element of G(x,y);
 * for every object x a designated element $$\mathrm{id}_x$$ of G(x,x);
 * for each triple of objects x, y, and z a function $$\mathrm{comp}_{x,y,z} : G(y, z)\times G(x, y) \rightarrow G(x, z): (g, f) \mapsto gf$$;
 * for each pair of objects x, y a function $$\mathrm{inv}: G(x, y) \rightarrow G(y, x): f \mapsto f^{-1}$$ satisfying, for any f : x → y, g : y → z, and h : z → w:
 * $$f\ \mathrm{id}_x = f$$ and $$\mathrm{id}_y\ f = f$$;
 * $$(h g) f = h (g f)$$;
 * $$f f^{-1} = \mathrm{id}_y$$ and $$f^{-1} f = \mathrm{id}_x$$.

If f is an element of G(x,y) then x is called the source of f, written s(f), and y is called the target of f, written t(f).

A groupoid G is sometimes denoted as $$G_1 \rightrightarrows G_0$$, where $$G_1$$ is the set of all morphisms, and the two arrows $$G_1 \to G_0$$ represent the source and the target.

More generally, one can consider a groupoid object in an arbitrary category admitting finite fiber products.

Comparing the definitions
The algebraic and category-theoretic definitions are equivalent, as we now show. Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G(x,y) (i.e. the sets of morphisms from x to y). Then $$\mathrm{comp}$$ and $$\mathrm{inv}$$ become partial operations on G, and $$\mathrm{inv}$$ will in fact be defined everywhere. We define ∗ to be $$\mathrm{comp}$$ and −1 to be $$\mathrm{inv}$$, which gives a groupoid in the algebraic sense. Explicit reference to G0 (and hence to $$\mathrm{id}$$) can be dropped.

Conversely, given a groupoid G in the algebraic sense, define an equivalence relation $$\sim$$ on its elements by $$a \sim b$$ iff a ∗ a−1 = b ∗ b−1. Let G0 be the set of equivalence classes of $$\sim$$, i.e. $$G_0:=G/\!\!\sim$$. Denote a ∗ a−1 by $$1_x$$ if $$a\in G$$ with $$x\in G_0$$.

Now define $$G(x, y)$$ as the set of all elements f such that $$1_x*f*1_y$$ exists. Given $$f \in G(x,y)$$ and $$g \in G(y, z),$$ their composite is defined as $$gf:=f*g \in G(x,z)$$. To see that this is well defined, observe that since $$(1_x*f)*1_y$$ and $$1_y*(g*1_z)$$ exist, so does $$(1_x*f*1_y)*(g*1_z)=f*g$$. The identity morphism on x is then $$1_x$$, and the category-theoretic inverse of f is f−1.

Sets in the definitions above may be replaced with classes, as is generally the case in category theory.

Vertex groups and orbits
Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G(x,x), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

The orbit of a groupoid G at a point $$x \in X$$ is given by the set $$s(t^{-1}(x)) \subseteq X$$ containing every point that can be joined to x by a morphism in G. If two points $$x$$ and $$y$$ are in the same orbits, their vertex groups $$G(x)$$ and $$G(y)$$ are isomorphic: if $$f$$ is any morphism from $$x$$ to $$y$$, then the isomorphism is given by the mapping $$g\to fgf^{-1}$$.

Orbits form a partition of the set X, and a groupoid is called transitive if it has only one orbit (equivalently, if it is connected as a category). In that case, all the vertex groups are isomorphic (on the other hand, this is not a sufficient condition for transitivity; see the section below for counterexamples).

Subgroupoids and morphisms
A subgroupoid of $$G \rightrightarrows X$$ is a subcategory $$H \rightrightarrows Y$$ that is itself a groupoid. It is called wide or full if it is wide or full as a subcategory, i.e., respectively, if $$X = Y$$ or $$G(x,y)=H(x,y)$$ for every $$x,y \in Y$$.

A groupoid morphism is simply a functor between two (category-theoretic) groupoids.

Particular kinds of morphisms of groupoids are of interest. A morphism $$p: E \to B$$ of groupoids is called a fibration if for each object $$x$$ of $$E$$ and each morphism $$b$$ of $$B$$ starting at $$p(x)$$ there is a morphism $$e$$ of $$E$$ starting at $$x$$ such that $$p(e)=b$$. A fibration is called a covering morphism or covering of groupoids if further such an $$e$$ is unique. The covering morphisms of groupoids are especially useful because they can be used to model covering maps of spaces.

It is also true that the category of covering morphisms of a given groupoid $$B$$ is equivalent to the category of actions of the groupoid $$B$$ on sets.

Topology
Given a topological space $$X$$, let $$G_0$$ be the set $$X$$. The morphisms from the point $$p$$ to the point $$q$$ are equivalence classes of continuous paths from $$p$$ to $$q$$, with two paths being equivalent if they are homotopic. Two such morphisms are composed by first following the first path, then the second; the homotopy equivalence guarantees that this composition is associative. This groupoid is called the fundamental groupoid of $$X$$, denoted $$\pi_1(X)$$ (or sometimes, $$\Pi_1(X)$$). The usual fundamental group $$\pi_1(X,x)$$ is then the vertex group for the point $$x$$.

The orbits of the fundamental groupoid $$\pi_1(X)$$ are the path-connected components of $$X$$. Accordingly, the fundamental groupoid of a path-connected space is transitive, and we recover the known fact that the fundamental groups at any base point are isomorphic. Moreover, in this case, the fundamental groupoid and the fundamental groups are equivalent as categories (see the section below for the general theory).

An important extension of this idea is to consider the fundamental groupoid $$\pi_1(X,A)$$ where $$A\subset X$$ is a chosen set of "base points". Here $$\pi_1(X,A)$$ is a (wide) subgroupoid of $$\pi_1(X)$$, where one considers only paths whose endpoints belong to $$A$$. The set $$A$$ may be chosen according to the geometry of the situation at hand.

Equivalence relation
If $$X$$ is a setoid, i.e. a set with an equivalence relation $$\sim$$, then a groupoid "representing" this equivalence relation can be formed as follows: The vertex groups of this groupoid are always trivial; moreover, this groupoid is in general not transitive and its orbits are precisely the equivalence classes. There are two extreme examples:
 * The objects of the groupoid are the elements of $$X$$;
 * For any two elements $$x$$ and $$y$$ in $$X$$, there is a single morphism from $$x$$ to $$y$$ (denote by $$(y,x)$$) if and only if $$x\sim y$$;
 * The composition of $$(z,y)$$ and $$(y,x)$$ is $$(z,x)$$.

 * If every element of $$X$$ is in relation with every other element of $$X$$, we obtain the pair groupoid of $$X$$, which has the entire $$X \times X$$ as set of arrows, and which is transitive.
 * If every element of $$X$$ is only in relation with itself, one obtains the unit groupoid, which has $$X$$ as set of arrows, $$s = t = id_X$$, and which is completely intransitive (every singleton $$\{x\}$$ is an orbit).

Examples

 * If $$f: X_0 \to Y$$ is a smooth surjective submersion of smooth manifolds, then $$X_0\times_YX_0 \subset X_0\times X_0$$ is an equivalence relation since $$Y$$ has a topology isomorphic to the quotient topology of $$X_0$$ under the surjective map of topological spaces. If we write, $$X_1 = X_0\times_YX_0$$ then we get a groupoid"$X_1 \rightrightarrows X_0$"which is sometimes called the banal groupoid of a surjective submersion of smooth manifolds.
 * If we relax the reflexivity requirement and consider partial equivalence relations, then it becomes possible to consider semidecidable notions of equivalence on computable realisers for sets. This allows groupoids to be used as a computable approximation to set theory, called PER models. Considered as a category, PER models are a cartesian closed category with natural numbers object and subobject classifier, giving rise to the effective topos introduced by Martin Hyland.

Čech groupoid
A Čech groupoid p. 5 is a special kind of groupoid associated to an equivalence relation given by an open cover $$\mathcal{U} = \{U_i\}_{i\in I}$$ of some manifold $$X$$. Its objects are given by the disjoint union "$\mathcal{G}_0 = \coprod U_i$," and its arrows are the intersections "$\mathcal{G}_1 = \coprod U_{ij}$." The source and target maps are then given by the induced maps $$\begin{align} s = \phi_j: U_{ij} \to U_j\\ t = \phi_i: U_{ij} \to U_i \end{align}$$ and the inclusion map"$\varepsilon: U_i \to U_{ii}$"giving the structure of a groupoid. In fact, this can be further extended by setting"$\mathcal{G}_n = \mathcal{G}_1\times_{\mathcal{G}_0} \cdots \times_{\mathcal{G}_0}\mathcal{G}_1$"as the $$n$$-iterated fiber product where the $$\mathcal{G}_n$$ represents $$n$$-tuples of composable arrows. The structure map of the fiber product is implicitly the target map, since $$\begin{matrix} U_{ijk} & \to & U_{ij} \\ \downarrow & & \downarrow \\ U_{ik} & \to & U_{i} \end{matrix}$$ is a cartesian diagram where the maps to $$U_i$$ are the target maps. This construction can be seen as a model for some ∞-groupoids. Also, another artifact of this construction is k-cocycles"$[\sigma] \in \check{H}^k(\mathcal{U},\underline{A})$"for some constant sheaf of abelian groups can be represented as a function"$\sigma:\coprod U_{i_1\cdots i_k} \to A$"giving an explicit representation of cohomology classes.

Group action
If the group $$G$$ acts on the set $$X$$, then we can form the action groupoid (or transformation groupoid) representing this group action as follows:
 * The objects are the elements of $$X$$;
 * For any two elements $$x$$ and $$y$$ in $$X$$, the morphisms from $$x$$ to $$y$$ correspond to the elements $$g$$ of $$G$$ such that $$gx = y$$;
 * Composition of morphisms interprets the binary operation of $$G$$.

More explicitly, the action groupoid is a small category with $$\mathrm{ob}(C)=X$$ and $$\mathrm{hom}(C)=G\times X$$ and with source and target maps $$s(g,x) = x$$ and $$t(g,x) = gx$$. It is often denoted $$G \ltimes X$$ (or $$X\rtimes G$$ for a right action). Multiplication (or composition) in the groupoid is then $$(h,y)(g,x) = (hg,x)$$ which is defined provided $$y=gx$$.

For $$x$$ in $$X$$, the vertex group consists of those $$(g,x)$$ with $$gx=x$$, which is just the isotropy subgroup at $$x$$ for the given action (which is why vertex groups are also called isotropy groups). Similarly, the orbits of the action groupoid are the orbit of the group action, and the groupoid is transitive if and only if the group action is transitive.

Another way to describe $$G$$-sets is the functor category $$[\mathrm{Gr},\mathrm{Set}]$$, where $$\mathrm{Gr}$$ is the groupoid (category) with one element and isomorphic to the group $$G$$. Indeed, every functor $$F$$ of this category defines a set $$X=F(\mathrm{Gr})$$ and for every $$g$$ in $$G$$ (i.e. for every morphism in $$\mathrm{Gr}$$) induces a bijection $$F_g$$ : $$X\to X$$. The categorical structure of the functor $$F$$ assures us that $$F$$ defines a $$G$$-action on the set $$G$$. The (unique) representable functor $$F$$ : $$\mathrm{Gr} \to \mathrm{Set}$$ is the Cayley representation of $$G$$. In fact, this functor is isomorphic to $$\mathrm{Hom}(\mathrm{Gr},-)$$ and so sends $$\mathrm{ob}(\mathrm{Gr})$$ to the set $$\mathrm{Hom}(\mathrm{Gr},\mathrm{Gr})$$ which is by definition the "set" $$G$$ and the morphism $$g$$ of $$\mathrm{Gr}$$ (i.e. the element $$g$$ of $$G$$) to the permutation $$F_g$$ of the set $$G$$. We deduce from the Yoneda embedding that the group $$G$$ is isomorphic to the group $$\{F_g\mid g\in G\}$$, a subgroup of the group of permutations of $$G$$.

Finite set
Consider the group action of $$\mathbb{Z}/2$$ on the finite set $$X = \{-2, -1, 0, 1, 2\}$$ which takes each number to its negative, so $$-2 \mapsto 2$$ and $$1 \mapsto -1$$. The quotient groupoid $$[X/G]$$ is the set of equivalence classes from this group action $$\{[0],[1],[2]\}$$, and $$[0]$$ has a group action of $$\mathbb{Z}/2$$ on it.

Quotient variety
Any finite group $$ G $$ that maps to $$ GL(n) $$ gives a group action on the affine space $$ \mathbb{A}^n $$ (since this is the group of automorphisms). Then, a quotient groupoid can be of the form $$ [\mathbb{A}^n/G] $$, which has one point with stabilizer $$ G $$ at the origin. Examples like these form the basis for the theory of orbifolds. Another commonly studied family of orbifolds are weighted projective spaces $$\mathbb{P}(n_1,\ldots, n_k)$$ and subspaces of them, such as Calabi–Yau orbifolds.

Fiber product of groupoids
Given a diagram of groupoids with groupoid morphisms

\begin{align} & & X \\ & & \downarrow \\ Y &\rightarrow & Z \end{align} $$

where $$ f:X\to Z $$ and $$ g:Y\to Z $$, we can form the groupoid $$ X\times_ZY $$ whose objects are triples $$ (x,\phi,y) $$, where $$ x \in \text{Ob}(X) $$, $$ y \in \text{Ob}(Y) $$, and $$ \phi: f(x) \to g(y) $$ in $$ Z $$. Morphisms can be defined as a pair of morphisms $$ (\alpha,\beta) $$ where $$ \alpha: x \to x' $$ and $$ \beta: y \to y' $$ such that for triples $$ (x,\phi,y), (x',\phi',y') $$, there is a commutative diagram in $$ Z $$ of $$ f(\alpha):f(x) \to f(x') $$, $$ g(\beta):g(y) \to g(y') $$ and the $$ \phi,\phi' $$.

Homological algebra
A two term complex

C_1 \overset{d}{\rightarrow}C_0 $$ of objects in a concrete Abelian category can be used to form a groupoid. It has as objects the set $$C_0$$ and as arrows the set $$C_1\oplus C_0$$; the source morphism is just the projection onto $$C_0$$ while the target morphism is the addition of projection onto $$C_1$$ composed with $$d$$ and projection onto $$C_0$$. That is, given $$c_1 + c_0 \in C_1\oplus C_0$$, we have

t(c_1 + c_0) = d(c_1) + c_0. $$ Of course, if the abelian category is the category of coherent sheaves on a scheme, then this construction can be used to form a presheaf of groupoids.

Puzzles
While puzzles such as the Rubik's Cube can be modeled using group theory (see Rubik's Cube group), certain puzzles are better modeled as groupoids.

The transformations of the fifteen puzzle form a groupoid (not a group, as not all moves can be composed). This groupoid acts on configurations.

Mathieu groupoid
The Mathieu groupoid is a groupoid introduced by John Horton Conway acting on 13 points such that the elements fixing a point form a copy of the Mathieu group M12.

Relation to groups
If a groupoid has only one object, then the set of its morphisms forms a group. Using the algebraic definition, such a groupoid is literally just a group. Many concepts of group theory generalize to groupoids, with the notion of functor replacing that of group homomorphism.

Every transitive/connected groupoid - that is, as explained above, one in which any two objects are connected by at least one morphism - is isomorphic to an action groupoid (as defined above) $$(G, X)$$. By transitivity, there will only be one orbit under the action.

Note that the isomorphism just mentioned is not unique, and there is no natural choice. Choosing such an isomorphism for a transitive groupoid essentially amounts to picking one object $$x_0$$, a group isomorphism $$h$$ from $$G(x_0)$$ to $$G$$, and for each $$x$$ other than $$x_0$$, a morphism in $$G$$ from $$x_0$$ to $$x$$.

If a groupoid is not transitive, then it is isomorphic to a disjoint union of groupoids of the above type, also called its connected components (possibly with different groups $$G$$ and sets $$X$$ for each connected component).

In category-theoretic terms, each connected component of a groupoid is equivalent (but not isomorphic) to a groupoid with a single object, that is, a single group. Thus any groupoid is equivalent to a multiset of unrelated groups. In other words, for equivalence instead of isomorphism, one does not need to specify the sets $$X$$, but only the groups $$G.$$ For example,

 * The fundamental groupoid of $$X$$ is equivalent to the collection of the fundamental groups of each path-connected component of $$X$$, but an isomorphism requires specifying the set of points in each component;
 * The set $$X$$ with the equivalence relation $$\sim$$ is equivalent (as a groupoid) to one copy of the trivial group for each equivalence class, but an isomorphism requires specifying what each equivalence class is:
 * The set $$X$$ equipped with an action of the group $$G$$ is equivalent (as a groupoid) to one copy of $$G$$ for each orbit of the action, but an isomorphism requires specifying what set each orbit is.

The collapse of a groupoid into a mere collection of groups loses some information, even from a category-theoretic point of view, because it is not natural. Thus when groupoids arise in terms of other structures, as in the above examples, it can be helpful to maintain the entire groupoid. Otherwise, one must choose a way to view each $$G(x)$$ in terms of a single group, and this choice can be arbitrary. In the example from topology, one would have to make a coherent choice of paths (or equivalence classes of paths) from each point $$p$$ to each point $$q$$ in the same path-connected component.

As a more illuminating example, the classification of groupoids with one endomorphism does not reduce to purely group theoretic considerations. This is analogous to the fact that the classification of vector spaces with one endomorphism is nontrivial.

Morphisms of groupoids come in more kinds than those of groups: we have, for example, fibrations, covering morphisms, universal morphisms, and quotient morphisms. Thus a subgroup $$H$$ of a group $$G$$ yields an action of $$G$$ on the set of cosets of $$H$$ in $$G$$ and hence a covering morphism $$p$$ from, say, $$K$$ to $$G$$, where $$K$$ is a groupoid with vertex groups isomorphic to $$H$$. In this way, presentations of the group $$G$$ can be "lifted" to presentations of the groupoid $$K$$, and this is a useful way of obtaining information about presentations of the subgroup $$H$$. For further information, see the books by Higgins and by Brown in the References.

Category of groupoids
The category whose objects are groupoids and whose morphisms are groupoid morphisms is called the groupoid category, or the category of groupoids, and is denoted by Grpd.

The category Grpd is, like the category of small categories, Cartesian closed: for any groupoids $$H,K$$ we can construct a groupoid $$\operatorname{GPD}(H,K)$$ whose objects are the morphisms $$ H \to K $$ and whose arrows are the natural equivalences of morphisms. Thus if $$ H,K $$ are just groups, then such arrows are the conjugacies of morphisms. The main result is that for any groupoids $$ G,H,K $$ there is a natural bijection

$$\operatorname{Grpd}(G \times H, K) \cong \operatorname{Grpd}(G, \operatorname{GPD}(H,K)).$$

This result is of interest even if all the groupoids $$ G,H,K $$ are just groups.

Another important property of Grpd is that it is both complete and cocomplete.

Relation to Cat
The inclusion $$i : \mathbf{Grpd} \to \mathbf{Cat}$$ has both a left and a right adjoint:

 * $$ \hom_{\mathbf{Grpd}}(C[C^{-1}], G) \cong \hom_{\mathbf{Cat}}(C, i(G)) $$
 * $$ \hom_{\mathbf{Cat}}(i(G), C) \cong \hom_{\mathbf{Grpd}}(G, \mathrm{Core}(C)) $$

Here, $$C[C^{-1}]$$ denotes the localization of a category that inverts every morphism, and $$\mathrm{Core}(C)$$ denotes the subcategory of all isomorphisms.

Relation to sSet
The nerve functor $$N : \mathbf{Grpd} \to \mathbf{sSet}$$ embeds Grpd as a full subcategory of the category of simplicial sets. The nerve of a groupoid is always a Kan complex.

The nerve has a left adjoint
 * $$ \hom_{\mathbf{Grpd}}(\pi_1(X), G) \cong \hom_{\mathbf{sSet}}(X, N(G)) $$

Here, $$\pi_1(X)$$ denotes the fundamental groupoid of the simplicial set X.

Groupoids in Grpd
There is an additional structure which can be derived from groupoids internal to the category of groupoids, double-groupoids. Because Grpd is a 2-category, these objects form a 2-category instead of a 1-category since there is extra structure. Essentially, these are groupoids $$\mathcal{G}_1,\mathcal{G}_0$$ with functors"$s,t: \mathcal{G}_1 \to \mathcal{G}_0$"and an embedding given by an identity functor"$i:\mathcal{G}_0 \to\mathcal{G}_1$"One way to think about these 2-groupoids is they contain objects, morphisms, and squares which can compose together vertically and horizontally. For example, given squares $$\begin{matrix} \bullet & \to & \bullet \\ \downarrow & & \downarrow \\ \bullet & \xrightarrow{a} & \bullet \end{matrix} $$ and $$\begin{matrix} \bullet & \xrightarrow{a} & \bullet \\ \downarrow & & \downarrow \\ \bullet & \to & \bullet \end{matrix}$$ with $$a$$ the same morphism, they can be vertically conjoined giving a diagram $$\begin{matrix} \bullet & \to & \bullet \\ \downarrow & & \downarrow \\ \bullet & \xrightarrow{a} & \bullet \\ \downarrow & & \downarrow \\ \bullet & \to & \bullet \end{matrix}$$ which can be converted into another square by composing the vertical arrows. There is a similar composition law for horizontal attachments of squares.

Groupoids with geometric structures
When studying geometrical objects, the arising groupoids often carry a topology, turning them into topological groupoids, or even some differentiable structure, turning them into Lie groupoids. These last objects can be also studied in terms of their associated Lie algebroids, in analogy to the relation between Lie groups and Lie algebras.

Groupoids arising from geometry often possess further structures which interact with the groupoid multiplication. For instance, in Poisson geometry one has the notion of a symplectic groupoid, which is a Lie groupoid endowed with a compatible symplectic form. Similarly, one can have groupoids with a compatible Riemannian metric, or complex structure, etc.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Groupoid


text:
Galliard

The galliard (gaillarde; gagliarda) was a form of Renaissance dance and music popular all over Europe in the 16th century. It is mentioned in dance manuals from England, Portugal, France, Spain, Germany, and Italy.

Dance form
The galliard is not an improvised dance, but rather, it consists of choreographed patterns of steps, which occupy one or more measures of music. In one measure, a galliard typically has five steps; in French such a basic step is called a cinq pas and in Italy, cinque passi. This is sometimes written in English sources as sinkapace. These steps are: right, left, right, left, cadence.

The galliard is an athletic dance, characterised by leaps, jumps, hops and other similar figures. The main feature that defines a galliard step is a large jump, after which the dancer lands with one leg ahead of the other. This jump is called a cadence, and the final landing is called the posture. The cadence is typically preceded by three quick hops with alternating feet. The sources generally describe movement patterns starting on the left foot, then repeating it starting with the right foot. A galliard pattern may also last twice as long, or more, which would involve 11 steps, or 17 steps.

The galliard was a favourite dance of Queen Elizabeth I of England, and although it is a relatively vigorous dance, in 1589 when the Queen was aged in her mid-fifties, John Stanhope of the Privy Chamber reported, "the Queen is so well as I assure you, six or seven galliards in a morning, besides music and singing, is her ordinary exercise."

While most commonly being an entire dance, the galliard's steps are used within many other forms of dance. For example, 16th-century Italian dances in Fabritio Caroso's (1581) and Cesare Negri's (1602) dance manuals often have a galliard section.

One special step used during a galliard is lavolta, a step which involves an intimate, close hold between a couple, with the woman being lifted into the air and the couple turning 270 degrees, within one six-beat measure. Lavolta was considered by some dancing masters as an inappropriate dance.

Another special step used during a galliard is the tassel kick ("salto del fiocco"). These steps are found in Negri's manual and involve a galliard step usually (though not always) ending with a spin. The easier steps involve single spins of 180 or 360 degrees; later, more difficult steps involve multiple sequential spins and spins of up to at least 540 degrees. During the spin, the dancer kicks out to touch a tassel suspended between knee and waist height.

Musical form

Musical compositions in the galliard form appear to have been written and performed after the dance fell out of popular use. In musical compositions, the galliard often filled the role of an after dance written in 6, which followed and mimicked another piece (sometimes a pavane) written in 4. The distinctive 6 beats to the phrase can still be heard today in songs such as "God Save the King".

General sources

 * Caroso, Fabritio (1581). Il ballarino. 2 volumes. Venice: Francesco Ziletti. Facsimile reprint in one volume, Monuments of Music and Music Literature in Facsimile. second series: Music Literature, 46, New York: Broude Brothers, 1967.
 * Negri, Cesare (1602). Le Gratie d'amore. Milan. Facsimile reprints, (1) Bibliotheca musica Bononiensis, Sez. 2, n. 104, Bologna: Forni Editore, 1969; (2) Monuments of Music and Music Literature in Facsimile. second series: Music Literature, no. 141, New York: Broude Bros., 1969.

title: Galliard


text:
General surgery

General surgery is a surgical specialty that focuses on alimentary canal and abdominal contents including the esophagus, stomach, small intestine, large intestine, liver, pancreas, gallbladder, appendix and bile ducts, and often the thyroid gland. General surgeons also deal with diseases involving the skin, breast, soft tissue, trauma, peripheral artery disease and hernias and perform endoscopic as such as gastroscopy, colonoscopy and laparoscopic procedures.

Scope
General surgeons may sub-specialise into one or more of the following disciplines:

Trauma surgery
In many parts of the world including North America, Australia and the United Kingdom, the overall responsibility for trauma care falls under the auspices of general surgery. Some general surgeons obtain advanced training in this field (most commonly surgical critical care) and specialty certification surgical critical care. General surgeons must be able to deal initially with almost any surgical emergency. Often, they are the first port of call to critically ill or gravely injured patients, and must perform a variety of procedures to stabilize such patients, such as thoracostomy, cricothyroidotomy, compartment fasciotomies and emergency laparotomy or thoracotomy to stanch bleeding. They are also called upon to staff surgical intensive care units or trauma intensive care units.

All general surgeons are trained in emergency surgery. Bleeding, infections, bowel obstructions and organ perforations are the main problems they deal with. Cholecystectomy, the surgical removal of the gallbladder, is one of the most common surgical procedures done worldwide. This is most often done electively, but the gallbladder can become acutely inflamed and require an emergency operation. Infections and rupture of the appendix and small bowel obstructions are other common emergencies.

Laparoscopic surgery
This is a relatively new specialty dealing with minimal access techniques using cameras and small instruments inserted through 3- to 15-mm incisions. Robotic surgery is now evolving from this concept (see below). Gallbladders, appendices, and colons can all be removed with this technique. Hernias are also able to be repaired laparoscopically. Bariatric surgery can be performed laparoscopically and there a benefits of doing so to reduce wound complications in obese patients. General surgeons that are trained today are expected to be proficient in laparoscopic procedures.

Colorectal surgery
General surgeons treat a wide variety of major and minor colon and rectal diseases including inflammatory bowel diseases (such as ulcerative colitis or Crohn's disease), diverticulitis, colon and rectal cancer, gastrointestinal bleeding and hemorrhoids.

Upper Gastrointestinal Surgery
General surgeons can specialise in Upper Gastro-intestinal (or foregut) surgery, which includes the surgical treatment of diseases of the stomach and oesophagus, liver, pancreas and gallbladder. In the UK, Upper GI surgeons can subspecialise further as benign surgeons, dealing with hiatus hernias and gallbladder diseases, bariatric surgeons, providing surgical care for weight management and metabolic diseases, or oesophago-gastric surgeons, dealing with complex problems related to the upper gastrointestinal tract (the foregut), including cancer. Surgical care of complex liver and pancreatic problems (including liver cancer and pancreatic cancer) is undertaken by Hepatobiliary and Pancreatic Surgery sub-specialists.

Breast surgery
General surgeons perform a majority of all non-cosmetic breast surgery from lumpectomy to mastectomy, especially pertaining to the evaluation, diagnosis and treatment of breast cancer.

Vascular surgery
General surgeons can perform vascular surgery if they receive special training and certification in vascular surgery. Otherwise, these procedures are typically performed by vascular surgery specialists. However, general surgeons are capable of treating minor vascular disorders.

Endocrine surgery
General surgeons are trained to remove all or part of the thyroid and parathyroid glands in the neck and the adrenal glands just above each kidney in the abdomen. In many communities, they are the only surgeon trained to do this. In communities that have a number of subspecialists, other subspecialty surgeons may assume responsibility for these procedures.

Transplant surgery
Responsible for all aspects of pre-operative, operative, and post-operative care of abdominal organ transplant patients. Transplanted organs include liver, kidney, pancreas, and more rarely small bowel.

Surgical oncology
Surgical oncologist refers to a general surgical oncologist (a specialty of a general surgeon), but thoracic surgical oncologists, gynecologist and so forth can all be considered surgeons who specialize in treating cancer patients. The importance of training surgeons who sub-specialize in cancer surgery lies in evidence, supported by a number of clinical trials, that outcomes in surgical cancer care are positively associated to surgeon volume (i.e., the more cancer cases a surgeon treats, the more proficient he or she becomes, and his or her patients experience improved survival rates as a result). This is another controversial point, but it is generally accepted, even as common sense, that a surgeon who performs a given operation more often, will achieve superior results when compared with a surgeon who rarely performs the same procedure. This is particularly true of complex cancer resections such as pancreaticoduodenectomy for pancreatic cancer, and gastrectomy with extended (D2) lymphadenectomy for gastric cancer. Surgical oncology is generally a 2-year fellowship following completion of a general surgery residency (5–7 years).

Cardiothoracic surgery
Most cardiothoracic surgeons in the U.S. (D.O. or M.D.) first complete a general surgery residency (typically 5–7 years), followed by a cardiothoracic surgery fellowship (typically 2–3 years). However, new programmes are currently offering cardiothoracic surgery as a residency (6–8 years).

Pediatric surgery
Pediatric surgery is a subspecialty of general surgery. Pediatric surgeons do surgery on patients under age 18. Pediatric surgery is 5–7 years of residency and a 2-3 year fellowship.

Trends
In the 2000s, minimally invasive surgery became more prevalent. Considerable enthusiasm has been built around robot-assisted surgery (also known as robotic surgery), despite a lack of data suggesting it has significant benefits that justify its cost.

Training
In Canada, Australia, New Zealand, and the United States general surgery is a five to seven year residency and follows completion of medical school, either MD, MBBS, MBChB, or DO degrees. In Australia and New Zealand, a residency leads to eligibility for Fellowship of the Royal Australasian College of Surgeons. In Canada, residency leads to eligibility for certification by and Fellowship of the Royal College of Physicians and Surgeons of Canada, while in the United States, completion of a residency in general surgery leads to eligibility for board certification by the American Board of Surgery or the American Osteopathic Board of Surgery which is also required upon completion of training for a general surgeon to have operating privileges at most hospitals in the United States.

In the United Kingdom, surgical trainees may apply to enter training after five years of medical school and two years of the Foundation Programme. During the two year core surgical training programme ("phase 1"), doctors are required to sit the Membership of the Royal College of Surgeons (MRCS) examination. On award of the MRCS by one of the four surgical colleges, surgeons may hold the title 'Mister' or 'Miss/Ms./Mrs' rather than doctor. This tradition dates back hundreds of years in the United Kingdom from when only physicians attended medical school and surgeons did not, but were rather associated with barbers in the Barber Surgeon's Guild. The tradition is also present in many Commonwealth countries including New Zealand and some states of Australia. After completion of phase 1 training, trainees may apply for a nationally awarded Higher Surgical Training (HST) programme, which lasts six years and is now divided into two further phases (phases 2 and 3). Trainees are expected to declare a sub-specialty before the end of phase 2, and training during phase 3 focusses on that sub-specialty. Before the end of HST, the examination for Fellowship of the Royal College of Surgeons (FRCS) must be taken in general surgery plus the subspeciality. Upon completion of training, the surgeon will be eligible for entry on the GMC Specialist Register. They may then apply to work both in the NHS and independent sector as a consultant surgeon, although many trainees complete further fellowships. The implementation of the European Working Time Directive limited UK surgical residents to an average 48-hour working week.

title: General surgery