Theorems · Theorem · category theory

SheafOfModules.pushforward_comp_id

∀ {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),
  SheafOfModules.pushforwardComp (CategoryTheory.CategoryStruct.id S) φ =
    (SheafOfModules.pushforward φ).isoWhiskerLeft (SheafOfModules.pushforwardId S) ≪≫
      (SheafOfModules.pushforward φ).rightUnitor

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuous