Theorems · Theorem · category theory

PresheafOfModules.naturality_apply

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
  {M₁ M₂ : PresheafOfModules R} (f : M₁ ⟶ M₂) {X Y : Cᵒᵖ} (g : X ⟶ Y) (x : ↑(M₁.obj X)),
  (CategoryTheory.ConcreteCategory.hom (f.app Y)) ((CategoryTheory.ConcreteCategory.hom (M₁.map g)) x) =
    (CategoryTheory.ConcreteCategory.hom (M₂.map g)) ((CategoryTheory.ConcreteCategory.hom (f.app X)) x)

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category