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. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...

ic structures including

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

and

universal algebra Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study ...

; *

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

; *

Homotopical algebra In mathematics, homotopical algebra is a collection of concepts comprising the ''nonabelian'' aspects of homological algebra as well as possibly the abelian aspects as special cases. The ''homotopical'' nomenclature stems from the fact that a c ...

; *

Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

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 invariants that classify topological spaces up to homeomorphism, though usually most classify ...

categorical topology In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continu ...

, 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 structure theory of 3-manifolds and 4-manifolds, knot th ...

; * Categorical logic and

set theory Set theory is the branch of mathematical logic that studies 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 mathematics, is mostly concern ...

in the categorical context such as algebraic set theory; *

Foundations of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...

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 notio ...

; * Abstract geometry, including

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, 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