Theorems · Theorem · category theory

PresheafOfModules.map_smul

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
  (M : PresheafOfModules R) {X Y : Cᵒᵖ} (f : X ⟶ Y) (r : ↑(R.obj X)) (m : ↑(M.obj X)),
  (CategoryTheory.ConcreteCategory.hom (M.map f)) (r • m) =
    (CategoryTheory.ConcreteCategory.hom (R.map f)) r • (CategoryTheory.ConcreteCategory.hom (M.map f)) m

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf

Cited by

5 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category