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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. The category of sets is the most basic and the most commonly used category in mathematics. Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of this category and/or restrict the arrows to functions of a particular kind. The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps. The empty set serves as the initial object in Set with empty functions as morphisms. Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element as morphisms. There are thus no zero objects in Set.
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