In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

generalization of the notion of a category. The study of such generalizations is known as higher category theory. Quasi-categories were introduced by Boardman...

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

categories. Category Functor Natural transformation Homological algebra Diagram chasing Topos theory Enriched category theory Higher category theory Categorical...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

in the category of sets). A topos can also be used to represent a logical theory. Mathematics portal Enriched category Higher category theory Quantaloid...

Higher Topos Theory is a treatise on the theory of ∞-categories written by American mathematician Jacob Lurie. In addition to introducing Lurie's new...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...

In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

small category to an abelian category are abelian as well. These stability properties make them inevitable in homological algebra and beyond; the theory has...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...

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

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

In mathematics, especially (higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian...

In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms...

In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e...

foams in loop quantum gravity, applications of higher categories to physics, and applied category theory. Additionally, Baez is known on the World Wide...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general...

In category theory, a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle...

In category theory, a branch of mathematics, a closed category is a special kind of category. In a locally small category, the external hom (x, y) maps...

theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics...