Direct limit

Common card · No. 400995

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 A i {\displaystyle A_{i}} , where i {\displaystyle i} ranges over some directed set I {\displaystyle I} , is denoted by lim → ⁡ A i {\displaystyle \varinjlim A_{i}} . This notation...

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