Normal category: Difference between revisions
(New page: ==Definition== A '''normal category''' is a category enriched over the monoidal category of pointed sets satisfying the condition that every monomorphism...) |
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{{pointed sets-enriched category property}} | |||
{{preadditive category property}} | |||
==Definition== | ==Definition== | ||
===For a category enriched over pointed sets=== | |||
A '''normal category''' is a [[category]] [[enriched category|enriched]] over the [[monoidal category of pointed sets]] satisfying the condition that every [[monomorphism]] is [[normal monomorphism|normal]]. | A '''normal category''' is a [[category]] [[enriched category|enriched]] over the [[monoidal category of pointed sets]] satisfying the condition that every [[monomorphism]] is [[normal monomorphism|normal]]. | ||
===For a preadditive category=== | |||
A [[preadditive category]] is termed a '''normal category''' if every [[monomorphism]] in it is [[normal monomorphism|normal]]. | |||
Latest revision as of 06:59, 26 December 2008
Template:Pointed sets-enriched category property
This article defines a preadditive category property: a property that can be evaluated to true/false given a preadditive category.
View a complete list of preadditive category properties|Get preadditive category property lookup help |Get exploration suggestions
VIEW RELATED: Preadditive category property implications | Preadditive category property non-implications | Preadditive category metaproperty satisfactions | Preadditive category metaproperty dissatisfactions | Preadditive category property satisfactions |Preadditive category property dissatisfactions
Definition
For a category enriched over pointed sets
A normal category is a category enriched over the monoidal category of pointed sets satisfying the condition that every monomorphism is normal.
For a preadditive category
A preadditive category is termed a normal category if every monomorphism in it is normal.