Category Set - Definition

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

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.