# 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.

This is known as a bijection. Bijectivity is a more specific version of isomorphism, specific to Set - the category of all sets.

## References¶

## Backlinks¶

- CT: Isomorphism
- Types have a cardinality
- In type theory a type has a cardinality. The cardinality for a given type is the number of possible values. A cardinality can be finite or infinite. A pair of types with the same cardinality will always be isomorphic.