Definition:Category of Sets

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


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

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

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 Finite Sets
 * Category of Pointed Sets