Theorems · Theorem · category theory

CategoryTheory.ModObj.mul_smul_self_flip_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M : C}
  [inst_2 : CategoryTheory.MonObj M] (X : C) [inst_3 : CategoryTheory.ModObj M X] {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft M CategoryTheory.ModObj.smul)
      (CategoryTheory.CategoryStruct.comp CategoryTheory.ModObj.smul h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator M M X).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.MonObj.mul X)
        (CategoryTheory.CategoryStruct.comp CategoryTheory.ModObj.smul h))

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonObjCategoryTheory.ModObj