Theorems · Definition · category theory

SheafOfModules.pullback

{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.pushforward φ).IsRightAdjoint] →
                        CategoryTheory.Functor (SheafOfModules S) (SheafOfModules R)

The pullback functor SheafOfModules S ⥤ SheafOfModules R induced by a morphism of sheaves of rings S ⟶ (F.sheafPushforwardContinuous RingCat.{u} J K).obj R, defined as the left adjoint functor to the pushforward, when it exists.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous

Cited by

12 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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