This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: * Categories of

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

ic structures including

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

and

universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures. For instance, rather than considering groups or rings as the object of stud ...

; *

Homological algebra Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precurs ...

; * Homotopical algebra; *

Topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

using categories, including

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

, categorical topology, quantum topology,

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, ...

; *

Categorical logic __NOTOC__ Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. In broad terms, cate ...

and

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

in the categorical context such as algebraic set theory; *

Foundations of mathematics Foundations of mathematics are the mathematical logic, logical and mathematics, mathematical framework that allows the development of mathematics without generating consistency, self-contradictory theories, and to have reliable concepts of theo ...

building on categories, for instance

topos theory In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion ...

; * Abstract geometry, including

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, 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

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
* * George Whitehead
Fifty years of homotopy theory
* Haynes Miller
The origin of sheaf theory
{{DEFAULTSORT:Timeline Of Category Theory And Related Mathematics Category theory Higher category theory Category theory and related mathematics