# Colimit

In

mathematics, the

category theory concept of

**colimit**, also known as a

**direct limit** or

**inductive limit**, is

dual to the notion of a

limit (

*inverse* or

*projective* limit). It is a rather general formulation of the idea of 'gluing together' mathematical objects. A typical example would be the free product with amalgamation of

groups.

The general definition of a colimit is given on the limit page. Special cases of colimits, each dual to a special case of limits, include coproduct, coequaliser, pushout.