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Locally finitely presentable category

From Cattheory

Revision as of 01:22, 10 December 2008 by Vipul (talk | contribs) (New page: ==Definition== A '''locally finitely presentable category''' is a locally small category that satisfies the following conditions: * It is [[defining ingredient::cocomplete category|c...)

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Definition

A locally finitely presentable category is a locally small category that satisfies the following conditions:

It is cocomplete: it contains all small colimits.
There exists a set of finitely presentable objects such that every object in the category is a directed colimit of objects in that set.

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