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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.