Theorems · Theorem · category theory

CategoryTheory.unit_obj_eq_map_unit

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (i : CategoryTheory.Functor D C) [inst_2 : CategoryTheory.Reflective i] (X : C),
  (CategoryTheory.reflectorAdjunction i).unit.app (i.obj ((CategoryTheory.reflector i).obj X)) =
    i.map ((CategoryTheory.reflector i).map ((CategoryTheory.reflectorAdjunction i).unit.app X))

For a reflective functor i (with left adjoint L), with unit η, we have η_iL = iL η.

Defined in

Mathlib.CategoryTheory.Adjunction.Reflective

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Reflective