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

categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer science also rely on category theory,...

of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides...

higher category theory, the concept of higher categorical structures, such as (∞-categories), allows for a more robust treatment of homotopy theory, enabling...

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

category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...

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

popularised by Barry Mitchell (1965)'s influential Theory of categories. Cf. e.g., https://blog.juliosong.com/linguistics/mathematics/category-theory-notes-9/...

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

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

In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...

specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms...

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, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function. Given a category C {\displaystyle...

Conferences: Applied category theory Symposium on Compositional Structures (SYCO) Books: Picturing Quantum Processes Categories for Quantum Theory An Invitation...

analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by Jacob Lurie (2009). Quasi-categories are certain...

concrete categories, such as the category of groups or the category of topological spaces. Category of topological spaces Set theory Small set (category theory)...

Especially for higher categories, the concepts from algebraic topology are also used in the category theory. For that see also glossary of algebraic topology...

In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...

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 category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism...

definitions. For instance, the K-theory is a 'universal additive invariant' of dg-categories and small stable ∞-categories. The motivation for this notion...

In category theory, a branch of mathematics, a presheaf on a category C {\displaystyle C} is a functor F : C o p → S e t {\displaystyle F\colon C^{\mathrm...

In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances...

traditional theory of categories, like linguist Eugenio Coseriu and other proponents of the structural semantics paradigm. In this prototype theory, any given...

In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...

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

although a category may have many distinct skeletons, any two skeletons are isomorphic as categories, so up to isomorphism of categories, the skeleton of a category...

into monoidal categories. Monoidal categories can be seen as a generalization of these and other examples. Every (small) monoidal category may also be viewed...