Category of Sets

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. The arrows or morphisms between sets A and B are all functions from A to B. Care must be taken in the definition of Set to avoid set-theoretic paradoxes.

Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of the category of sets and/or restrict the arrows to functions of a particular kind.

Read more about Category Of Sets:  Properties of The Category of Sets, Foundations For The Category of Sets

Other articles related to "category of sets, set, sets":

Category Of Sets - Foundations For The Category of Sets
... In Zermelo–Fraenkel set theory the collection of all sets is not a set this follows from the axiom of foundation ... One refers to collections that are not sets as proper classes ... One can't handle proper classes as one handles sets in particular, one can't write that those proper classes belong to a collection (either a set or a proper class) ...

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