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

Categories Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally *Category of being *Categories (Aristotle), ''Categories'' (Aristotle) *Category (Kant) ...

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 term ''a ...

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 (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 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 ...

; *

Topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

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 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 contin ...

quantum topology Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology. Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associat ...

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 __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, categ ...

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 conce ...

in the categorical context such as algebraic set theory; *

Foundations of mathematics Foundations of mathematics is the study of the philosophy, 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 natu ...

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, 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 Categorical may refer to: * Categorical imperative, a concept in philosophy developed by Immanuel Kant * Categorical theory, in mathematical logic * Morley's categoricity theorem, a mathematical theorem in model theory * Categorical data analysis ...

, etc. * Quantization related to category theory, in particular

categorical quantization Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably Monoidal category, monoidal category theory. The primitive objects of study are physical Quantu ...

; *

Categorical physics Categorical may refer to: * Categorical imperative, a concept in philosophy developed by Immanuel Kant * Categorical theory, in mathematical logic * Morley's categoricity theorem, a mathematical theorem in model theory * Categorical data analysis ...

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