Objects (category theory)

objects used in category theory branch of mathematics

In category theory, a branch of mathematics, a subobject is, roughly speaking, an object that sits inside another object in the same category. The notion is a generalization of concepts such as subsets from set theory, subgroups from group theory, and subspaces from topology. Since the detailed structure of objects is immaterial in category theory, the definition of subobject relies on a morphism that describes how one object sits inside another, rather than relying on the use of elements.

object 𝑃 in an abelian category such that hom(𝑃,–) is an exact functor to the category of abelian groups

monoid in certain category-theoretic category

analogue of the definition of a group inside an arbitrary category

categorical generalization of a function space in set theory

in category theory