Definition:Category of Sets

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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.


The reason to call $\mathbf{Set}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.

Also see