Theorems · Definition · algebraic geometry

SheafOfModules.QuasicoherentData.IsFinitePresentation.casesOn

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : ∀ (X : C), CategoryTheory.HasWeakSheafify (J.over X) AddCommGrpCat] →
          [inst_2 : ∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] →
            {M : SheafOfModules R} →
              {q : M.QuasicoherentData} →
                {motive : q.IsFinitePresentation → Sort u_2} →
                  (t : q.IsFinitePresentation) →
                    ((isFinite_presentation : ∀ (i : q.I), (q.presentation i).IsFinite) → motive ⋯) → motive t

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective