The Category of Sets

The category of sets, denoted \(\text{Set}\), is the locally-small Category whose objects are all sets and whose morphisms are all functions between those sets. It is one of the most commonly-used categories in Category Theory, especially within the context of The Yoneda Lemma.

A Functor whose codomain is the category of sets is said to be set-valued. A Contravariant Functor which is set-valued is called a Pre-Sheaf.