Timeline of category theory and related mathematics

This is a timeline of category theory and related mathematics. By related mathematics is meant first hand
* Homological algebra
* Homotopical algebra
* Topology using categories, especially algebraic topology
* Categorical logic
* Foundations of mathematics building on categories, for instance topos theory
* Abstract geometry (including algebraic geometry, but not only)
* Quantization related to category theory, in particular categorical quantization
* Categorical physics relevant for mathematics

Timeline

* 1940 Kurt Gödel-Paul Bernays — Classes (set theory)
* 1944 Samuel Eilenberg — Modern definition of singular homology and cohomology
* 1945 Saunders Mac Lane-Samuel Eilenberg — Start of category theory (axioms for categories,functors,natural transformations)
* 1945 Norman Steenrod-Samuel Eilenberg — Axioms for homology and cohomology: Eilenberg-Steenrod axioms
* 1945 Jean Leray — Sheaf theory
* 1946 Jean Leray — Spectral sequences
* 1950 John Henry Whitehead — Outlines algebraic homotopy program
* 1956 Henri Cartan-Samuel Eilenberg — Influential book: Homological algebra
* 1957 Alexander Grothendieck — Influential paper: Tohoku
* 1958 Alexander Grothendieck — Starts new foundation of algebraic geometry by schemes
* 1958 Roger Godement — Monads (category theory) (then called standard constructions)
* 1958 Daniel Kan — Adjoint functors
* 1958 Alexander Grothendieck — Fibred categories
* 1960 Daniel Kan — Kan extensions
* 1963 Saunders Mac Lane — Monoidal categories
* 1963 Alexander Grothendieck — Grothendieck toposes
* 1963 William Lawvere — Categorical logic and Lawvere theories
* 1963 Jean-Louis Verdier — Triangulated categories and triangulated functors
* 1963 Jean Giraud — Giraud big theorem
* 1963 Charles Ehresmann — Internal categories, double categories and 2-categories
* 1964 Alexander Grothendieck — Grothendieck topology on categories
* 1965 Max Kelly-Samuel Eilenberg — Enriched category theory
* 1966 Alexander Grothendieck — Crystals (differential equation)
* 1967 Jean Bénabou — Bicategories (weak 2-categories)
* 1967 William Lawvere — Synthetic differential geometry
* 1967 Simon Kochen-Ernst Specker — Kochen-Specker theorem
* 1967 Jean-Louis Verdier — Derived categories and derived functors
* 1967 Daniel Quillen — Model categories
* 1969 Pierre Deligne-David Mumford — Deligne-Mumford stacks
* 1969 William Lawvere — Doctrines (category theory)
* 1970 William Lawvere — Toposes
* 1971 Jean Giraud — Gerbes
* 1971 William Lawvere-Myles Tierney — Lawvere-Tierney topology on a topos
* 1972 Max Kelly — Clubs (category theory) and coherence (category theory)
* 1972 Alexander Grothendieck — Universes (mathematics) for sets
* 1972 Jean Bénabou-Ross Street — Cosmoses (category theory)
* 1972 Peter May — Operads
* 1972 William Mitchell-Jean Bénabou - Internal Mitchell-Bénabou language for toposes
* 1974 Jean Bénabou — Logic of fibred categories
* 1974 Graeme Segal — Segal categories
* 1975 Saul Kripke-Andre Joyal — Kripke-Joyal semantics
* 1978 Andre Joyal — Joyal combinatorial species in enumerative combinatorics
* 1981 Shigeru Mukai — Mukai-Fourier transform
* 1983 Alexander Grothendieck — Writes about 600 pages letter pursuing stacks to Daniel Quillen about his mathematical visions
* 1983 Alexander Grothendieck — First appearance of strict n-categories and strict ∞-categories in pursuing stacks
* 1983 Alexander Grothendieck — Fundamental infinity groupoid appear in pursuing stacks
* 1985 Andre Joyal-Ross Street — Braided monoidal categories
* 1986 Alexander Grothendieck — Motives (algebraic geometry)
* 1987 Ross Street — First definition of weak n-category
* 1987 Andre Joyal-Ross Street-Mei Chee Shum — Ribbon monoidal categories
* 1988 Edward Witten — Axioms for topological quantum field theory TQFT
* 1989 Hans Baues — Innfluential book: Algebraic homotopy
* 1990 Peter Freyd — Allegories (category theory)
* 1990 Nicolai Reshetikhin-Vladimir Turaev — Reshetikhin-Turaev invariants of knots from modular monoidal categories of representations of quantum groups
* 1992 Yves Diers — Axiomatic categorical geometry
* 1992 Saunders Mac Lane-Leke Moerdijk — Influential book: Sheaves in geometry and logic
* 1993 Kenji Fukaya — A_∞-categories (Fukaya category)
* 1993 Daniel Freed — New view on TQFT using modular tensor categories that unifies 3 approach to TQFT (modular categories from path integrals)
* 1994 Francis Borceux — Handbook of categorical algebra (3 volumes)
* 1994 Maxim Kontsevich — Formulates homological mirror symmetry conjecture
* 1995 john Baez-James Dolan — Introduces the periodic table of mathematics
* 1995 Valentin Lychagin — Categorical quantization
* 1998 John Baez-James Dolan — Microcosm principle
* 1999 Mikhail Khovanov — Khovanov homology (categorization of the Jones polynomial)
* 1999 Vladimir Voevodsky-Fabien Morel — Constructs the homotopy category of schemes
* 2002 Bertrand Toen-Gabriele Vezzosi — Homotopical algebraic geometry
* 2002 Peter Johnstone — Influential book: sketches of an elephant - a topos theory compendium (2/3 volumes published)
* 2004 Ross Street-Brian Day — Quantum categories

References