hom-set

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

hom-set (plural hom-sets)

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

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

• morphism set

• Thomes