Commit 2024-07-01 22:27 cf6699f8
View on Github →feat(CategoryTheory): if LR is abstractly isomorphic to the identity functor, then the unit is an isomorphism. (#14017)
This PR proves that to show that the unit of an adjunction L ⊣ R
is an isomorphism (i.e. that L is fully faithful), it is enough to give an arbitrary isomorphism L ⋙ R ≅ 𝟭 C
, and the dual result.
To do this, we give a general way to transport (co)monad structures on functors along isomorphisms of functors.