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. Backlinks¶ CT: Isomorphism Isomorphism is the generalisation of the concept of bijection from the category Set to other categories. A pair of types with the same cardinality will always be isomorphic This is known as a bijection. Bijectivity is a more specific version of isomorphism, specific to Set - the category of all sets. Lenses can be seen as a bijection with some residual A Lens a b is a bijection between a and (b, r), where r is a - b. This represents a Lens as an isomorphism. Given (b, r) one could construct a.