Theorems · Definition · category theory

PresheafOfModules.pullback

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {F : CategoryTheory.Functor C D} →
          {R : CategoryTheory.Functor Dᵒᵖ RingCat} →
            {S : CategoryTheory.Functor Cᵒᵖ RingCat} →
              (φ : S ⟶ F.op.comp R) →
                [(PresheafOfModules.pushforward φ).IsRightAdjoint] →
                  CategoryTheory.Functor (PresheafOfModules S) (PresheafOfModules R)

The pullback functor PresheafOfModules S ⥤ PresheafOfModules R induced by a morphism of presheaves of rings S ⟶ F.op ⋙ R, defined as the left adjoint functor to the pushforward, when it exists.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback

Cited by

3 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightAdjoint