Group homomorphism

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Definition

A group homomorphism is a function, $f:G\rightarrow H$ between two groups, $(G,\times)$ and $(H,*)$ such that:

• $\forall a,b\in G[f(a\times b)=f(a)*f(b)]$

These are homomorphisms in the categorical sense (of the $\mathrm{GROUP}$ category)