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.

Also see

• Category of Finite Sets is Category
• Category of Sets
• Results about the category of finite sets can be found here.

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.1$