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I understand the fact that grp theory textbooks defined Hom(G, H) as (g + h) u forms a group homomorphism. I wanted to know if there is any notion of homomorphism as [itex]\Sigma_{I} g_{i}[/itex] where each [itex]g_{i}[/itex] is a homomorphism and I is an infinite index set. If so how is it defined.

Thx