Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.hom_inv_actionHomLeft

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.MonoidalCategory C]
  [inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] {x y : C} (f : x ≅ y) (z : D),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f.hom z)
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f.inv z) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj x z)

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

1 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.MonoidalLeftAction