Editing Limit (category theory) (section)

{{Short description|Mathematical concept}}
{{More footnotes|date=March 2013}} 
In [[category theory]], a branch of [[mathematics]], the abstract notion of a '''limit''' captures the essential properties of universal constructions such as [[product (category theory)|products]], [[pullback (category theory)|pullbacks]] and [[inverse limit]]s.  The [[duality (category theory)|dual notion]] of a '''colimit''' generalizes constructions such as [[disjoint union]]s, [[direct sum]]s, [[coproduct]]s, [[pushout (category theory)|pushout]]s and [[direct limit]]s.

Limits and colimits, like the strongly related notions of [[universal property|universal properties]] and [[adjoint functors]], exist at a high level of abstraction. In order to understand them, it is helpful to first study the specific examples these concepts are meant to generalize.