Naïve set theory MOC

Surjectivity, injectivity, and bijectivity

Surjective, injective, and bijective functions are epimorphisms, monomorphisms, and isomorphisms respectively in . Thus the morphisms of any concrete category may be described as such, but these concepts may not align exactly (for example, there exist bijectivity continuous functions that are not homeomorphisms). Specifically, given a function

• is surjective iff for every there exists such that #m/def/general
  • Equivalently, there exists a right-inverse.
  • A surjective function induces an Equivalence relation.
• is injective iff . #m/def/general
  • Equivalently, there exists a left-inverse.
• is bijective iff it is surjective and injective. #m/def/general
  • Equivalently, there exists a unique ambidextrous inverse.

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