# Definition:Category of Sets

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## 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

## Sources

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