Definition:Category of Finite Sets

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


 * objects: All finite sets;
 * morphisms: All mappings between finite sets.

This forms a metacategory, as shown on Category of Finite Sets is Category.

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

Also see

 * Category of Sets