Editing Subobject (section)

In [[category theory]], a branch of [[mathematics]], a '''subobject''' is, roughly speaking, an [[Object (category theory)|object]] that sits inside another object in the same [[category (mathematics)|category]].  The notion is a generalization of concepts such as [[subset]]s from [[set theory]], [[subgroup]]s from [[group theory]],<ref name="Mac Lane">Mac Lane, p. 126</ref> and [[subspace (topology)|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.

The [[dual (category theory)|dual]] concept to a subobject is a '''{{visible anchor|quotient object}}'''. This generalizes concepts such as [[quotient set]]s, [[quotient group]]s, [[quotient space (topology)|quotient spaces]], [[quotient graph]]s, etc.