hom-set

Etymology
Short for "homomorphism set", because in some categories the morphisms are homomorphisms.

Noun

 * 1)  The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category.

Usage notes

 * A hom-set may be denoted as $$\mathcal{C}(X,Y)$$ for objects X and Y in a category $$\mathcal{C}$$. It may also be denoted as $$\text{Hom}_\mathcal{C}(X,Y)$$; or, letting $$\mathcal{C}$$ be implicit, simply as $$\text{Hom}(X,Y)$$.

Synonyms

 * morphism set