Category

Object

Morphism

Functor

A mapping between objects in a category

A function between sets

A relation between elements of a set

A transformation between vector spaces

The morphism that maps each object to itself

The morphism that maps each object to the zero object

The morphism that maps each object to the terminal object

The morphism that maps each object to its inverse

A mapping between categories

A function between sets

A relation between elements of a set

A transformation between vector spaces

A result that relates functors to natural transformations

A result that relates categories to sets

A result that relates morphisms to objects

A result that relates functors to categories

A functor that has a right adjoint

A functor that has a left adjoint

A functor that has both a left and right adjoint

A functor that has neither a left nor right adjoint

A functor that maps a category to itself

A functor that maps a category to a set

A functor that maps a category to a category of functors

A functor that maps a category to a category of categories

A construction that combines a family of objects into a single object

A construction that combines a family of morphisms into a single morphism

A construction that combines a family of categories into a single category

A construction that combines a family of functors into a single functor

A construction that combines a family of objects into a single object

A construction that combines a family of morphisms into a single morphism

A construction that combines a family of categories into a single category

A construction that combines a family of functors into a single functor

The category whose objects are sets and whose morphisms are functions

The category whose objects are categories and whose morphisms are functors

The category whose objects are functors and whose morphisms are natural transformations

The category whose objects are categories of functors and whose morphisms are functors between categories of functors

The category whose objects are categories and whose morphisms are functors

The category whose objects are sets and whose morphisms are functions

The category whose objects are functors and whose morphisms are natural transformations

The category whose objects are categories of functors and whose morphisms are functors between categories of functors

The category whose objects are functors and whose morphisms are natural transformations

The category whose objects are categories and whose morphisms are functors

The category whose objects are sets and whose morphisms are functions

The category whose objects are categories of functors and whose morphisms are functors between categories of functors

The category whose objects are categories of functors and whose morphisms are functors between categories of functors

The category whose objects are functors and whose morphisms are natural transformations

The category whose objects are categories and whose morphisms are functors

The category whose objects are sets and whose morphisms are functions

A set of axioms that characterize the category of topological spaces

A set of axioms that characterize the category of groups

A set of axioms that characterize the category of rings

A set of axioms that characterize the category of fields