Suppose I want to refer to morphisms that all have the same graph $G$ as their target. What is the appropriate terminology to refer to these kind of morphisms.
"Morphisms with the same ending graph" Or "morphism with the same codomain". Any precise concise terminology for these kind of morphisms?
$Hom(-, G)$ can be used to denote the set of morphisms with codomain $G$. Conversely for $Hom(G, -)$.
However, you should be careful: I've also seen $Hom(-, G)$ used to denote the map which sends an object $A$ to the set $Hom(A, G)$ of morphisms from $A$ to $G$. Context makes it clear which meaning is intended, but it's an ambiguity worth pointing out.
(Ideally, there should be two different notations, but I've seen the same symbols used to denote each concept.)
