# 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
- 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.