Theorems · Theorem · category theory

CategoryTheory.TwoSquare.GuitartExact.whiskerHorizontal

∀ {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)
  {T' : CategoryTheory.Functor C₁ D₁} {B' : CategoryTheory.Functor C₂ D₂} [w.GuitartExact] (α : T ≅ T') (β : B ≅ B'),
  (w.whiskerHorizontal α.inv β.hom).GuitartExact

A 2-square stays Guitart exact if we replace the top and bottom functors by isomorphic functors. See also whiskerHorizontal_iff.

Defined in

Mathlib.CategoryTheory.GuitartExact.HorizontalComposition

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.TwoSquare.GuitartExact