Theorems · Theorem · category theory

SheafOfModules.pushforwardSections_unitHomEquiv

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : CategoryTheory.GrothendieckTopology C} {K : CategoryTheory.GrothendieckTopology D}
  {F : CategoryTheory.Functor C D} {S : CategoryTheory.Sheaf J RingCat} {R : CategoryTheory.Sheaf K RingCat}
  [inst_2 : F.IsContinuous J K] (φ : S ⟶ (F.sheafPushforwardContinuous RingCat J K).obj R) {M : SheafOfModules R}
  (f : SheafOfModules.unit R ⟶ M),
  SheafOfModules.pushforwardSections φ (M.unitHomEquiv f) =
    ((SheafOfModules.pushforward φ).obj M).unitHomEquiv
      (CategoryTheory.CategoryStruct.comp (SheafOfModules.unitToPushforwardObjUnit φ)
        ((SheafOfModules.pushforward φ).map f))

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree

Cited by

0 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuous