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

concept of limit in category theory. By working in the dual category, that is by reversing the arrows, an inverse limit becomes a direct limit or inductive...

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

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

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...

the limit depends on the system of homomorphisms. Direct limits are a special case of the concept of colimit in category theory. Direct limits are dual...

common throughout category theory for any binary equaliser. In the case of a preadditive category (a category enriched over the category of Abelian groups)...

Cokernel Pushout (category theory) Direct limit Biproduct Direct sum Preadditive category Additive category Pre-Abelian category Abelian category Exact sequence...

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

category theory, limits and colimits in an ∞-category generalize limits and colimits in a category. Like the counterparts in ordinary category theory...

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

In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely...

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

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

limit and direct limit in category theory. The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly...

In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in...

above Limit inferior and limit superior Limit of a net Limit point, in topological spaces Limit (category theory) Direct limit Inverse limit Limits (BDSM)...

a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many expositions...

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...

object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that...

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...

In the mathematical field of category theory, the category of sets, denoted by Set, is the category whose objects are sets. The arrows or morphisms between...

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...

category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C (where J is small) has a limit in...

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

{\displaystyle {\mathcal {F}}} turns colimits of such diagrams into limits. In some categories, it is possible to construct a sheaf by specifying only some of...

In category theory, a coequalizer (or coequaliser) is a generalization of a quotient by an equivalence relation to objects in an arbitrary category. It...

(2009). Direct limit – Special case of colimit in category theory Inverse limit – Construction in category theory completions in category theory Illusie, Luc...

In category theory and its applications to mathematics, a biproduct of a finite collection of objects, in a category with zero objects, is both a product...