# ACT4E Category Set - Definition

This is an exemplary page in which we define the category of sets and functions, called $\mathbf{Set}$.

###### Definition

The category of sets and functions $\mathbf{Set}$ is constituted of:

• Objects: all sets;
• Morphisms: Given sets $X$ and $Y$, the set $\text{Hom}_{\mathbf{Set}}(X,Y)$ is the set of all functions from $X$ to $Y$;
• Identity morphisms: Given a set $X$, its identity morphism $\text{id}_X$ is the identity function $X\to X$, $\text{id}_X(x)=x$;
• Composition operation: The composition operation is the usual composition of functions.