Direct limit
Special case of colimit in category theory / From Wikipedia, the free encyclopedia
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In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any category. The way they are put together is specified by a system of homomorphisms (group homomorphism, ring homomorphism, or in general morphisms in the category) between those smaller objects. The direct limit of the objects , where
ranges over some directed set
, is denoted by
. This notation suppresses the system of homomorphisms; however, the limit depends on the system of homomorphisms.
Direct limits are a special case of the concept of colimit in category theory. Direct limits are dual to inverse limits, which are a special case of limits in category theory.