Timeline of category theory and related mathematics

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 BernaysClasses (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 LeraySheaf theory
* 1946 Jean LeraySpectral 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 GodementMonads (category theory) (then called standard constructions)
* 1958 Daniel KanAdjoint functors
* 1958 Alexander GrothendieckFibred categories
* 1960 Daniel KanKan extensions
* 1963 Saunders Mac LaneMonoidal categories
* 1963 Alexander Grothendieck — Grothendieck toposes
* 1963 William LawvereCategorical logic and Lawvere theories
* 1963 Jean-Louis VerdierTriangulated categories and triangulated functors
* 1963 Jean GiraudGiraud big theorem
* 1963 Charles EhresmannInternal categories, double categories and 2-categories
* 1964 Alexander GrothendieckGrothendieck topology on categories
* 1965 Max Kelly-Samuel EilenbergEnriched category theory
* 1966 Alexander Grothendieck — Crystals (differential equation)
* 1967 Jean BénabouBicategories (weak 2-categories)
* 1967 William LawvereSynthetic differential geometry
* 1967 Simon Kochen-Ernst Specker — Kochen-Specker theorem
* 1967 Jean-Louis VerdierDerived categories and derived functors
* 1967 Daniel QuillenModel categories
* 1969 Pierre Deligne-David Mumford — Deligne-Mumford stacks
* 1969 William LawvereDoctrines (category theory)
* 1970 William LawvereToposes
* 1971 Jean GiraudGerbes
* 1971 William Lawvere-Myles TierneyLawvere-Tierney topology on a topos
* 1972 Max KellyClubs (category theory) and coherence (category theory)
* 1972 Alexander GrothendieckUniverses (mathematics) for sets
* 1972 Jean Bénabou-Ross StreetCosmoses (category theory)
* 1972 Peter MayOperads
* 1972 William Mitchell-Jean Bénabou - Internal Mitchell-Bénabou language for toposes
* 1974 Jean Bénabou — Logic of fibred categories
* 1974 Graeme SegalSegal categories
* 1975 Saul Kripke-Andre JoyalKripke-Joyal semantics
* 1978 Andre Joyal — Joyal combinatorial species in enumerative combinatorics
* 1981 Shigeru MukaiMukai-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 GrothendieckFundamental infinity groupoid appear in pursuing stacks
* 1985 Andre Joyal-Ross StreetBraided monoidal categories
* 1986 Alexander GrothendieckMotives (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 FreydAllegories (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 DolanMicrocosm principle
* 1999 Mikhail KhovanovKhovanov 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


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