Theorems · Inductive type · algebraic geometry

PresheafOfModules.Derivation

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : CategoryTheory.Functor Cᵒᵖ CommRingCat} →
          {F : CategoryTheory.Functor C D} →
            {R : CategoryTheory.Functor Dᵒᵖ CommRingCat} →
              PresheafOfModules (R.comp (CategoryTheory.forget₂ CommRingCat RingCat)) →
                (S ⟶ F.op.comp R) → Type (max (max u u₂) v)

Given a morphism of presheaves of commutative rings φ : S ⟶ F.op ⋙ R, this is the type of relative φ-derivation of a presheaf of R-modules M.

Defined in

Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf

Cited by

18 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category