Theorems · Theorem · category theory

CategoryTheory.ModObj.lift_leftSMul_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {M : C}
  [inst_2 : CategoryTheory.MonObj M] {X : C} [inst_3 : CategoryTheory.ModObj M X] (Z : C) (x : Z ⟶ X) (m : Z ⟶ M)
  {Z_1 : C} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj X X ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift m x)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.ModObj.leftSMul M X) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift (m • x) x) h

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.ModObj