SET (category)

Definition

The category [ilmath]\mathrm{SETS} [/ilmath] 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.

Subcategories

(Loads)

• [ilmath]\mathrm{GROUP} [/ilmath] - the category of all groups and group homomorphisms
  • [ilmath]\mathrm{AGROUP} [/ilmath] - a subcategory of [ilmath]\mathrm{GROUP} [/ilmath] consisting of all Abelian groups and their homomorphisms which are just the group homomorphisms between Abelian groups)
• [ilmath]\mathrm{TOP} [/ilmath] - 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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