(related to Motivation: Common Concepts Of Algebra: Substructures and Morphisms)
The following figure illustrates the connections between the different morphisms and their properties:
These words should help you to memorize the diagram:
"HIMSI" Homomorphism (Injective) Monomorphism (Surjective) Isomorphism
and
"DIA" enDomorphism epImorphism Automorphism.
From these words, it should be easier to rebuild the whole diagram from scratch.