Theorems · Theorem · category theory

CategoryTheory.TwoSquare.GuitartExact.whiskerVertical_iff

∀ {C₁ : Type u_1} {C₂ : Type u_2} {D₁ : Type u_4} {D₂ : Type u_5} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_4, u_4} D₁]
  [inst_3 : CategoryTheory.Category.{v_5, u_5} D₂] {T : CategoryTheory.Functor C₁ D₁} {L : CategoryTheory.Functor C₁ C₂}
  {R : CategoryTheory.Functor D₁ D₂} {B : CategoryTheory.Functor C₂ D₂} (w : CategoryTheory.TwoSquare T L R B)
  {L' : CategoryTheory.Functor C₁ C₂} {R' : CategoryTheory.Functor D₁ D₂} (α : L ≅ L') (β : R ≅ R'),
  (w.whiskerVertical α.hom β.inv).GuitartExact ↔ w.GuitartExact

A 2-square is Guitart exact iff it is so after replacing the left and right functors by isomorphic functors.

Defined in

Mathlib.CategoryTheory.GuitartExact.VerticalComposition

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category