Theorems · Theorem · category theory

CategoryTheory.ModObj.one_smul_assoc

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} {D : Type u₂}
  {inst_2 : CategoryTheory.Category.{v₂, u₂} D} {inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D}
  {M : C} {inst_4 : CategoryTheory.MonObj M} (X : D) [self : CategoryTheory.ModObj M X] {Z : D} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft CategoryTheory.MonObj.one X)
      (CategoryTheory.CategoryStruct.comp CategoryTheory.ModObj.smul h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionUnitIso X).hom h

The identity acts trivially.

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

0 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.ModObj