SET (category)

Definition

The category $\mathrm{SET}$ is the category that contains every set for its objects and every function (in the conventional sense, as mappings from 1 set to another) between those sets as the arrows of the category.

• Note: sometimes the $\mathrm{SET}$ category is AKA $\mathrm{SETS}$ (and the page SETS (category) redirects here)

Subcategories

(Loads)

• $\mathrm{GROUP}$ - the category of all groups and group homomorphisms
  • $\mathrm{AGROUP}$ - a subcategory of $\mathrm{GROUP}$ consisting of all Abelian groups and their homomorphisms which are just the group homomorphisms between Abelian groups)
• $\mathrm{TOP}$ - the category of all topological spaces, the arrows are continuous maps

Many more, rings, commutative rings, so forth.

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TODO: (More) exhaustive list

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