Category of sets

Definition

The category of sets, denoted $\operatorname {Set}$, is defined as follows:

• The objects of this category are sets.
• For any two sets $A,B$, $\operatorname {Set} (A,B)$ is defined as the set of all functions from $A$ to $B$.
• The identity morphism from any object to itself is defined as the identity map on that object.
• The composition of morphisms is defined by function composition.

The category of sets is a locally small category.