| Category Of Groups |
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The Monomorphism s in Grp are precisely the Injective homomorphisms, the Epimorphism s are precisely the Surjective homomorphisms, and the Isomorphism s are precisely the Bijective homomorphisms. The category Grp is both Complete And Co-complete . The Category-theoretical Product in Grp is just the Direct Product of groups while the Category-theoretical Coproduct in Grp is the Free Product of groups. The Zero Object s in Grp are the Trivial Group s (consisting of just an identity element). The Category Of Abelian Groups , Ab, is a Full Subcategory of '''Grp'''. It is an Abelian Category , but '''Grp''' is not. Indeed, '''Grp''' isn't even an Additive Category , because there is no natural way to define the "sum" of two group homomorphisms. |
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