Definition:Category of Sets

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

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