# 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.