Theorems · Theorem · category theory

SheafOfModules.pushforwardNatIso_inv

∀ {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 G : CategoryTheory.Functor C D} {T : CategoryTheory.Sheaf J RingCat} {S : CategoryTheory.Sheaf K RingCat}
  [inst_2 : F.IsContinuous J K] [inst_3 : G.IsContinuous J K] (φ : T ⟶ (G.sheafPushforwardContinuous RingCat J K).obj S)
  (α : F ≅ G),
  (SheafOfModules.pushforwardNatIso φ α).inv =
    CategoryTheory.CategoryStruct.comp
      (SheafOfModules.pushforwardNatTrans
        (CategoryTheory.CategoryStruct.comp φ
          ((CategoryTheory.Functor.sheafPushforwardContinuousNatTrans α.hom RingCat J K).app S))
        α.inv)
      (SheafOfModules.pushforwardCongr ⋯).hom

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuousCategoryTheory.Functor.IsContinuous