Theorems · Theorem · category theory

CategoryTheory.ModObj.comp_smul

∀ {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 Z' : C} (g : Z' ⟶ Z) (m : Z ⟶ M)
  (x : Z ⟶ X),
  CategoryTheory.CategoryStruct.comp g (m • x) =
    CategoryTheory.CategoryStruct.comp g m • CategoryTheory.CategoryStruct.comp g x

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.ModObj