Subobject Definition

(category theory) Given an object B, a subobject of it is an equivalence class of objects which relate to B through monomorphisms . (If a pair of monomorphisms with codomain B factor through each other, then their domains are isomorphic and thus belong to an equivalence class which defines a subobject of B). The subobject generalizes its interpretation in category Set as a set which is a subset (though an inclusion map, which is a monomorphism) of another set.