Definition:Category of Sets

Definition

The category of sets, denoted $\mathbf{Set}$ or $\mathbf{Sets}$ is the metacategory with:

Objects:		sets
Morphisms:		mappings
Composition:		composition of mappings
Identity morphisms:		identity mappings

Also known as

Some authors use a Germanic font to denote categories and write $\mathfrak{Set}$ instead.

As this is hard to read (when we don't know that it says "Set") we discourage this convention.

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 is Category
• Definition:Category of Finite Sets
• Definition:Category of Pointed Sets

Sources

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