Gregory Maxwell "Max" Kelly (5 June 1930 – 26 January 2007) was an Australian mathematician who worked on category theory.
Biography
Kelly was born in
Bondi, New South Wales
Bondi () is a suburb of eastern Sydney, in the state of New South Wales, Australia, seven kilometres east of the Sydney central business district, in the local government area of Waverley Council. It is often colloquially referred to as "Bon ...
, Australia, on 5 June 1930. He obtained his PhD at
Cambridge University
The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...
in homological algebra in 1957, publishing his first paper in that area in 1959, ''Single-space axioms for homology theory''. He taught in the Pure Mathematics department at the
University of Sydney
The University of Sydney (USYD), also known as Sydney University, or informally Sydney Uni, is a public research university located in Sydney, Australia. Founded in 1850, it is the oldest university in Australia and is one of the country's ...
from 1957 to 1966, rising from lecturer to reader. During 1963–1965 he was a visiting fellow at
Tulane University
Tulane University, officially the Tulane University of Louisiana, is a private research university in New Orleans, Louisiana. Founded as the Medical College of Louisiana in 1834 by seven young medical doctors, it turned into a comprehensive pub ...
and the
University of Illinois
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...
, where with
Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra.
Early life and education
He was born in Warsaw, Kingdom of Poland to ...
he formalized and developed the notion of an
enriched category In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category. It is motivated by the observation that, in many practical applications, the ho ...
based on intuitions then in the air about making the homsets of a category just as abstract as the objects themselves.
He subsequently developed the notion in considerably more detail in his 1982 monograph ''Basic Concepts of Enriched Category Theory''. Let be a
monoidal category
In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor
:\otimes : \mathbf \times \mathbf \to \mathbf
that is associative up to a natural isomorphism, and an object ''I'' that is both a left a ...
, and denote by -Cat the category of -enriched categories. Among other things, Kelly showed that -Cat has all weighted limits and colimits even when does not have all ordinary
limits and colimits
In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions su ...
. He also developed the enriched counterparts of
Kan extension
Kan extensions are Universal property, universal constructs in category theory, a branch of mathematics. They are closely related to Adjoint functors, adjoints, but are also related to Limit (category theory), limits and End (category theory), ends ...
s, density of the
Yoneda embedding
In mathematics, the Yoneda lemma is arguably the most important result in category theory. It is an abstract result on functors of the type ''morphisms into a fixed object''. It is a vast generalisation of Cayley's theorem from group theory (vie ...
, and essentially algebraic theories.
In 1967 Kelly was appointed Professor of Pure Mathematics at the
University of New South Wales
The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensiv ...
. In 1972 he was elected a
Fellow of the Australian Academy of Science
The Fellowship of the Australian Academy of Science is made up of about 500 Australian scientists.
Scientists judged by their peers to have made an exceptional contribution to knowledge in their field may be elected to Fellowship of the Academy ...
. He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1992. In 2001 he was awarded the Australian government's Centenary Medal. He continued to participate in the department as professorial fellow and professor emeritus until his death at age 76 on 26 January 2007.
Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations. His PhD students include
Ross Street
Ross Howard Street (born 29 September 1945, Sydney) is an Australian mathematician specialising in category theory.