Information AboutFull Subcategory |
| CATEGORIES ABOUT SUBCATEGORY | |
| category theory | |
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A full subcategory ''S'' of a category ''C'' is a subcategory of ''C'' such that for each objects ''A'' and ''B'' of ''S'', : The natural Functor from ''S'' of ''C'' that acts as the identity on objects and arrows is called the inclusion functor. It is always a Faithful Functor . The inclusion functor is Full if and only if ''S'' is a full subcategory. A Serre subcategory is a non-empty full subcategory ''S'' of an Abelian Category ''C'' such that for all short Exact Sequence s : in ''C'', ''M'' belongs to ''S'' if and only if both and do. This notion arises from Serre 's C-theory . SEE ALSO |
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