Theorems · Theorem · category theory

CategoryTheory.Mod.scalarRestriction_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 B : C} [inst_4 : CategoryTheory.MonObj A] [inst_5 : CategoryTheory.MonObj B] (f : A ⟶ B)
  [inst_6 : CategoryTheory.IsMonHom f] (M N : D) [inst_7 : CategoryTheory.ModObj B M]
  [inst_8 : CategoryTheory.ModObj B N] (g : M ⟶ N) [CategoryTheory.IsModHom B g], CategoryTheory.IsModHom A g

If g : M ⟶ N is a B-linear morphism of B-modules, then it induces an A-linear morphism when M and N have an A-module structure obtained by restricting scalars along a monoid morphism A ⟶ B.

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.MonoidalLeftActionCategoryTheory.MonObjCategoryTheory.MonObjCategoryTheory.IsMonHomCategoryTheory.ModObjCategoryTheory.ModObjCategoryTheory.IsModHom