Theorems · Definition · category theory

SheafOfModules.pushforwardNatIso

{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.pushforward φ ≅
                            SheafOfModules.pushforward
                              (CategoryTheory.CategoryStruct.comp φ
                                ((CategoryTheory.Functor.sheafPushforwardContinuousNatTrans α.hom RingCat J K).app S))

A natural isomorphism gives a natural isomorphism between the pushforward functors.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous

Cited by

2 results in Mathlib

Foundations

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

Assumes

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