Normal category

This article defines a preadditive category property: a property that can be evaluated to true/false given a preadditive category.
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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.