A subobject of is an isomorphism class of monomorphisms into . A quotient object is dually an isomorphism class of epimorphisms out of .
A category is well-powered when every object has only a set of subobjects. It is well-copowered when every object has only a set of quotient objects.
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A subobject is a term used in various fields such as mathematics, computer science, and programming, and its meaning can vary depending on the context. Here are a few interpretations: 1. **Mathematics**: In category theory, a subobject is a generalization of the concept of a subset. It refers to a monomorphism (injective morphism) from one object to another, essentially capturing the notion of a "part" of an object in a categorical framework.