Theorems · Definition · category theory

CategoryTheory.Mod.scalarRestriction

{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 B : C} →
              [inst_4 : CategoryTheory.MonObj A] →
                [inst_5 : CategoryTheory.MonObj B] →
                  (f : A ⟶ B) →
                    [CategoryTheory.IsMonHom f] → (M : D) → [CategoryTheory.ModObj B M] → CategoryTheory.ModObj A M

When M is a B-module in D and f : A ⟶ B is a morphism of internal monoid objects, M inherits an A-module structure via "restriction of scalars", i.e γ[A, M] = f ⊵ₗ M ≫ γ[B, M].

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

5 results in Mathlib

Foundations

Depth 11 from the axioms · uses propext, Quot.sound

Assumes

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