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.

Note

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