Theorems · Theorem · category theory

CategoryTheory.unitCompPartialBijective_symm_natural

∀ {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] (A : C) {B B' : C} (h : B ⟶ B')
  (hB : i.essImage B) (hB' : i.essImage B') (f : i.obj ((CategoryTheory.reflector i).obj A) ⟶ B),
  (CategoryTheory.unitCompPartialBijective A hB').symm (CategoryTheory.CategoryStruct.comp f h) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.unitCompPartialBijective A hB).symm f) h

Defined in

Mathlib.CategoryTheory.Adjunction.Reflective

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Reflective