Theorems · Theorem · category theory

CategoryTheory.eHom_whisker_cancel_inv

∀ (V : Type u') [inst : CategoryTheory.Category.{v', u'} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u}
  [inst_2 : CategoryTheory.Category.{v, u} C] [inst_3 : CategoryTheory.EnrichedOrdinaryCategory V C] {X Y Y₁ Z : C}
  (α : Y ≅ Y₁),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.eHomWhiskerLeft V X α.inv) (Y₁ ⟶[V] Z))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (X ⟶[V] Y) (CategoryTheory.eHomWhiskerRight V α.hom Z))
        (CategoryTheory.eComp V X Y Z)) =
    CategoryTheory.eComp V X Y₁ Z

Defined in

Mathlib.CategoryTheory.Enriched.Ordinary.Basic

Cited by

1 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.EnrichedOrdinaryCategory