Indeed, a homomorphism from A to B is an isomorphism from A to a subset of B. In other words, homomorphism is to injective as isomorphism is to bijective. So wh

Indeed, a homomorphism from A to B is an isomorphism from A to a subset of B. In other words, homomorphism is to injective as isomorphism is to bijective. So whether you say A is equivalent to B depends on how you define equivalent. For anyone curious, while Category Theory is very concerned with morphisms, they also come up in many other places. In particular, Abstract Algebra (groups and rings and such) may be a more approachable introduction to morphisms than Category Theory, and then Category Theory flows pretty naturally from the concepts of Abstract Algebra.