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 $a$.