Theorems · Theorem · category theory

PresheafOfModules.map_comp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
  (self : PresheafOfModules R) {X Y Z : Cᵒᵖ} (f : X ⟶ Y) (g : Y ⟶ Z),
  self.map (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (self.map f)
      (CategoryTheory.CategoryStruct.comp ((ModuleCat.restrictScalars (RingCat.Hom.hom (R.map f))).map (self.map g))
        ((ModuleCat.restrictScalarsComp' (RingCat.Hom.hom (R.map f)) (RingCat.Hom.hom (R.map g))
                (RingCat.Hom.hom (R.map (CategoryTheory.CategoryStruct.comp f g))) ⋯).inv.app
          (self.obj Z)))

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category