Homomorphism of Powers

Theorem
Let $\left({T_1, \odot_1}\right)$ and $\left({T_2, \odot_2}\right)$ be semigroups.

Let $\phi: \left({T_1, \odot_1}\right) \to \left({T_2, \odot_2}\right)$ be a (semigroup) homomorphism.