Definition:Category of Finite Sets

Definition
The category of finite sets, denoted $\mathbf{Finset}$ or $\mathbf{Sets}_{\text{fin}}$ is the metacategory with:

Note
The reason to call $\mathbf{Finset}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.

Also see

 * Category of Finite Sets is Category
 * Category of Sets