Group antihomomorphism ($f(gh)=f(h)f(g)$)

A group antihomomorphism between groups reverses multiplication: $f(gh)=f(h)f(g)$. Inversion $g\mapsto g^{-1}$ is an example. An antihomomorphism is a group homomorphism when the multiplication in the target is replaced by its reverse. In a nonabelian target the reversal matters: the group homomorphism and antihomomorphism identities generally differ.