# Max Kelly

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Australian mathematician

For the Australian rules footballer, see [Max Kelly (footballer)](/source/Max_Kelly_(footballer)).

Gregory Maxwell Kelly Born 5 June 1930 Died 26 January 2007(2007-01-26) (aged 76) Alma mater University of Cambridge Known for Enriched category theory Awards Centenary Medal Scientific career Fields Mathematics Institutions University of Sydney Thesis Topics in Homology Theory (1957) Doctoral advisor Shaun Wylie Doctoral students Ross Street

**Gregory Maxwell "Max" Kelly** (5 June 1930 – 26 January 2007) was an Australian mathematician who worked on [category theory](/source/Category_theory).

## Biography

Kelly was born in [Bondi, New South Wales](/source/Bondi%2C_New_South_Wales), [Australia](/source/Australia), on 5 June 1930.[1] He obtained his [PhD](/source/Doctor_of_Philosophy) at [Cambridge University](/source/Cambridge_University) in [homological algebra](/source/Homological_algebra) in 1957, publishing his first paper in that area in 1959, *Single-space axioms for homology theory*.[1][2] He taught in the Pure Mathematics department at the [University of Sydney](/source/University_of_Sydney) from 1957 to 1966, rising from lecturer to reader.[1] During 1963–1965 he was a visiting fellow at [Tulane University](/source/Tulane_University) and the [University of Illinois](/source/University_of_Illinois_at_Urbana-Champaign),[1] where with [Samuel Eilenberg](/source/Samuel_Eilenberg) he formalized and developed the notion of an [enriched category](/source/Enriched_category) based on intuitions then in the air about making the [homsets](/source/Hom_set) of a [category](/source/Category_(mathematics)) just as abstract as the objects themselves.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

He subsequently developed the notion in considerably more detail in his 1982 monograph *Basic Concepts of Enriched Category Theory*.[3] Let V {\displaystyle {\cal {V}}} be a [monoidal category](/source/Monoidal_category), and denote by V {\displaystyle {\cal {V}}} -Cat the category of V {\displaystyle {\cal {V}}} -enriched categories. Among other things, Kelly showed that V {\displaystyle {\cal {V}}} -Cat has all weighted limits and colimits even when V {\displaystyle {\cal {V}}} does not have all ordinary [limits and colimits](/source/Limits_and_colimits). He also developed the enriched counterparts of [Kan extensions](/source/Kan_extension), density of the [Yoneda embedding](/source/Yoneda_embedding), and essentially algebraic theories.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

In 1967 Kelly was appointed Professor of Pure Mathematics at the [University of New South Wales](/source/University_of_New_South_Wales).[1] In 1972 he was elected a [Fellow of the Australian Academy of Science](/source/Fellow_of_the_Australian_Academy_of_Science).[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1992.[1] In 2001 he was awarded the Australian government's [Centenary Medal](/source/Centenary_Medal). He continued to participate[*[dubious](https://en.wikipedia.org/wiki/Wikipedia:Accuracy_dispute#Disputed_statement) – [discuss](https://en.wikipedia.org/wiki/Talk:Max_Kelly#Dubious)*] in the department as professorial fellow and professor emeritus until his death at age 76 on 26 January 2007.[1]

Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] His PhD students include [Ross Street](/source/Ross_Street).[2]

## References

1. ^ [***a***](#cite_ref-mactutor_1-0) [***b***](#cite_ref-mactutor_1-1) [***c***](#cite_ref-mactutor_1-2) [***d***](#cite_ref-mactutor_1-3) [***e***](#cite_ref-mactutor_1-4) [***f***](#cite_ref-mactutor_1-5) [***g***](#cite_ref-mactutor_1-6) O'Connor, John J.; [Robertson, Edmund F.](/source/Edmund_F._Robertson), ["Max Kelly"](https://mathshistory.st-andrews.ac.uk/Biographies/Kelly_Max.html), *[MacTutor History of Mathematics Archive](/source/MacTutor_History_of_Mathematics_Archive)*, [University of St Andrews](/source/University_of_St_Andrews)

1. ^ [***a***](#cite_ref-mgp_2-0) [***b***](#cite_ref-mgp_2-1) [Gregory Maxwell (Max) Kelly](https://mathgenealogy.org/id.php?id=32935) at the [Mathematics Genealogy Project](/source/Mathematics_Genealogy_Project)

1. **[^](#cite_ref-3)** Kelly, Gregory Maxwell (1982). [*Basic Concepts of Enriched Category Theory*](http://tac.mta.ca/tac/reprints/articles/10/tr10abs.html). [Cambridge University Press](/source/Cambridge_University_Press). [ISBN](/source/ISBN_(identifier)) [978-0-521-28702-9](https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-28702-9).

## External links

- [Max Kelly's Perpetual Web Page](https://web.archive.org/web/20070217030315/http://www.maxkelly.com.au/main.php): a memorial page set up by Kelly's son Simon Kelly.

- ["In Memory of Max Kelly"](https://golem.ph.utexas.edu/category/2007/02/in_memory_of_max_kelly.html): a post at [*The n-Category Café*](https://golem.ph.utexas.edu/category/), containing praise from his fellow mathematicians

- [G. M. Kelly](https://dblp.org/pid/06/5208) at [DBLP](/source/DBLP_(identifier)) Bibliography Server

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Adapted from the Wikipedia article [Max Kelly](https://en.wikipedia.org/wiki/Max_Kelly) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Max_Kelly?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.