Injectivity¶ In set theory, injectivity is a property of a function. Given a function f : A \rightarrow B, if when supplied with every input in A f produces every possible output in B then f is injective. Backlinks¶ Range In Maths[^1], the range of a function is the set of all possible outputs within the Codomain. This might be smaller than the codomain itself if the function is not injective. A pair of types with the same cardinality will always be isomorphic There will always be a way of exhaustively mapping each value of type a to type b, injectively and surjectively when viewing the domain and the codomain as a set. Bijection In the category of sets, Set, a bijection is a morphism which is both injective and surjective. In it's generalised form, this is isomorphism.