Category theory MOC

Subcategory

A subcategory of a category is a category containing subclasses of objects and morphisms in , i.e. for any also and . cat It comes with the natural inclusion which is clearly a Faithful functor.

• A full subcategory is a subcategory of for which the inclusion functor is fully faithful, i.e. for all .
• A wide subcategory is a subcategory of containing all objects of .
• An essentially wide subcategory is a subcategory containing a skeleton category of .

Examples

• is a full subcategory of

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