Theorems · Theorem · category theory

CategoryTheory.TwoSquare.EquivalenceJ.functor_map

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} {C₄ : Type u₄} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  [inst_3 : CategoryTheory.Category.{v₄, u₄} C₄] {T : CategoryTheory.Functor C₁ C₂} {L : CategoryTheory.Functor C₁ C₃}
  {R : CategoryTheory.Functor C₂ C₄} {B : CategoryTheory.Functor C₃ C₄} (w : CategoryTheory.TwoSquare T L R B) {X₂ : C₂}
  {X₃ : C₃} (g : R.obj X₂ ⟶ B.obj X₃) {f₁ f₂ : w.StructuredArrowRightwards g} (φ : f₁ ⟶ f₂),
  (CategoryTheory.TwoSquare.EquivalenceJ.functor w g).map φ =
    CategoryTheory.CostructuredArrow.homMk
      (CategoryTheory.StructuredArrow.homMk (CategoryTheory.StructuredArrow.Hom.right φ).left ⋯) ⋯

Defined in

Mathlib.CategoryTheory.GuitartExact.Basic

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category