Theorems · Definition · category theory

PresheafOfModules.pullbackObjIsDefined

{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} →
              (S ⟶ F.op.comp R) → CategoryTheory.ObjectProperty (PresheafOfModules S)

Given a morphism of presheaves of rings φ : S ⟶ F.op ⋙ R, this is the property that the (partial) left adjoint functor of pushforward φ is defined on a certain object M : PresheafOfModules S.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category