Talk:Subcategory

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If a full subcategory contains all identity morphisms, and for every pair of id. morphisms it contains, it contains all morphisms between the corresponding objects, then what is the difference between a full subcategory and the original category? Is it so, that we take a "subset" of the objects, and a subcategory is required to contain only all identitiy morphisms of the objects in that subset? Mikolt 13:26, 9 Jul 2004 (UTC)

Yes, that's my understanding. A subcategory contains all identity morphisms between a subset of objects. For example, Ab is a full subcategory of Grp but Ring isn't (there are group homomorphisms between rings which aren't ring homomorphisms). The page seems worded badly, but this isn't my area of expertise. – Fropuff 15:46, 2004 Jul 9 (UTC)

It actually wasn't right, really; and was also too compressed. I've tried another kind of definition. Charles Matthews 16:43, 9 Jul 2004 (UTC)