Surjectivity

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• 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.