Theorems · Theorem · category theory

SheafOfModules.pullback_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)
  [inst_3 : (SheafOfModules.pushforward φ).IsRightAdjoint],
  SheafOfModules.pullbackComp φ (CategoryTheory.CategoryStruct.id R) =
    (SheafOfModules.pullback φ).isoWhiskerLeft (SheafOfModules.pullbackId R) ≪≫ (SheafOfModules.pullback φ).rightUnitor

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous

Cited by

1 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuousCategoryTheory.Functor.IsRightAdjoint