Locally finitely presentable category: Difference between revisions
(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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{{category property}} | |||
==Definition== | ==Definition== | ||
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* It is [[defining ingredient::cocomplete category|cocomplete]]: it contains all [[small colimit]]s. | * It is [[defining ingredient::cocomplete category|cocomplete]]: it contains all [[small colimit]]s. | ||
* There exists a ''set'' of [[finitely presentable object]]s such that every object in the category is a directed colimit of objects in that set. | * There exists a ''set'' of [[finitely presentable object]]s such that every object in the category is a directed colimit of objects in that set. | ||
==Relation with other properties== | |||
===Weaker properties=== | |||
* [[Stronger than::Locally presentable category]]: This is a category that is locally <math>\lambda</math>-presentable for some cardinal <math>\lambda</math>. | |||
* [[Stronger than::Cocomplete category]] | |||
Latest revision as of 01:24, 10 December 2008
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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 -presentable for some cardinal .
- Cocomplete category
