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...

also define a contravariant functor as a covariant functor on the opposite category C o p {\displaystyle C^{\mathrm {op} }} . Some authors prefer to write...

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...

equivalences correspond to their opposites, fibrations opposites of cofibrations and cofibrations opposites of fibrations. The category of topological spaces, Top...

Outline of category theory Timeline of category theory and related mathematics Applied category theory Some authors compose in the opposite order, writing...

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, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked...

can be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc. Let G...

prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular...

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...