hom-set

English

Etymology

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

Noun

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.

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

Anagrams

• Thomes