Locally finitely presentable category

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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.

Relation with other properties

Weaker properties

• Locally presentable category: This is a category that is locally $\lambda$-presentable for some cardinal $\lambda$.
• Cocomplete category