This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as:
Categories of abstract algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic and set theory in the categorical context such as algebraic set theory; Foundations of mathematics building on categories, for instance topos theory; Abstract geometry, including algebraic geometry, categorical noncommutative geometry, etc. Quantization related to category theory, in particular categorical quantization; Categorical physics relevant for mathematics. In this article, and in category theory in general, ∞ = ω.
Timeline to 1945: before the definitions
1945–1970
1971–1980
1981–1990
1991–2000
2001–present
See also EGA FGA SGA
Notes
References nLab, just as a higher-dimensional Wikipedia, started in late 2008; see nLab Zhaohua Luo; Categorical geometry homepage John Baez, Aaron Lauda; A prehistory of n-categorical physics Ross Street; An Australian conspectus of higher categories Elaine Landry, Jean-Pierre Marquis; Categories in context: historical, foundational, and philosophical Jim Stasheff; A survey of cohomological physics John Bell; The development of categorical logic Jean Dieudonné; The historical development of algebraic geometry Charles Weibel; History of homological algebra Peter Johnstone; The point of pointless topology Stasheff, Jim (January 21, 1996). "The Pre-History Of Operads". In Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.). Operads: Proceedings of Renaissance Conferences. Contemporary Mathematics. Vol. 202. Providence, Rhode Island: American Mathematical Society. pp. 9–14. CiteSeerX 10.1.1.25.5089. doi:10.1090/conm/202/02592. ISBN 0-8218-0513-4. ISSN 0271-4132. LCCN 96-37049. MR 1436913. Retrieved 2021-12-08. {{cite conference}}: Cite uses deprecated parameter |citeseerx= (help) George Whitehead; Fifty years of homotopy theory Haynes Miller; The origin of sheaf theory