Theorems · Theorem · category theory

CategoryTheory.Join.mapPairEquiv_unitIso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {C' : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} C'] {D' : Type u₄}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} D'] (e : C ≌ C') (e' : D ≌ D'),
  (CategoryTheory.Join.mapPairEquiv e e').unitIso =
    CategoryTheory.Join.mapPairId.symm ≪≫
      CategoryTheory.Join.mapIsoWhiskerRight e.unitIso (CategoryTheory.Functor.id D) ≪≫
        CategoryTheory.Join.mapIsoWhiskerLeft (e.functor.comp e.inverse) e'.unitIso ≪≫
          CategoryTheory.Join.mapPairComp e.functor e'.functor e.inverse e'.inverse

Defined in

Mathlib.CategoryTheory.Join.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category