Theorems · Theorem · category theory

CategoryTheory.ModObj.ofIso_smul

∀ {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} {N : C} [inst_5 : CategoryTheory.MonObj N] (e₁ : M ≅ N)
  [inst_6 : CategoryTheory.IsMonHom e₁.hom] {Y : D} (e₂ : X ≅ Y) [inst_7 : CategoryTheory.ModObj M X],
  CategoryTheory.ModObj.smul =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom e₁.inv e₂.inv)
      (CategoryTheory.CategoryStruct.comp CategoryTheory.ModObj.smul e₂.hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

0 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.MonoidalLeftActionCategoryTheory.MonObjCategoryTheory.MonObjCategoryTheory.IsMonHomCategoryTheory.ModObj