Theorems · Theorem · category theory

CategoryTheory.IsModHom.smul_hom

∀ {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}
  {A : C} {inst_4 : CategoryTheory.MonObj A} {M N : D} {inst_5 : CategoryTheory.ModObj A M}
  {inst_6 : CategoryTheory.ModObj A N} {f : M ⟶ N} [self : CategoryTheory.IsModHom A f],
  CategoryTheory.CategoryStruct.comp CategoryTheory.ModObj.smul f =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomRight A f)
      CategoryTheory.ModObj.smul

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

4 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.IsModHom