Natural transformation

Natural isomorphism

A natural isomorphism is an isomorphism in a functor category, cat i.e. a natural transformation 𝜂 ∈𝖣𝖢(𝐹,𝐺) such that 𝜂𝑋 :𝐹𝑋 →𝐺𝑋 is an isomorphism for all 𝑋 ∈𝖢. If such an isomorphism exists we write 𝐹 ≃𝐺.

The idea was first proposed in A general theory of natural equivalences, which is also the originating paper of category theory.

See Equivalence of categories

---

tidy | en | SemBr