Question

In definition of homomorphism identities are map to each other group theory

Answer 1

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With such an approach, morphisms in the category of groups are group homomorphisms and isomorphisms in this category are just group isomorphisms. Similarly for rings vector spaces etc.

A group homomorphism that is bijective; ie, injective and surjective. Its inverse is also a group homomorphism. In this case, the groups G and H are called isomorphic; they differ only in the notation of their elements and are identical for all practical purposes. Endomorphism.Isomorphism (in a narrow/algebraic sense) - a homomorphism which is 1-1 and onto. In other words: a homomorphism which has an inverse.

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