Theorems · Theorem · algebraic geometry

SheafOfModules.Presentation.ofIsIso_relations

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
  {R : CategoryTheory.Sheaf J RingCat} [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]
  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] {M N : SheafOfModules R} (f : M ⟶ N)
  [inst_3 : CategoryTheory.IsIso f] (σ : M.Presentation),
  (SheafOfModules.Presentation.ofIsIso f σ).relations =
    σ.relations.ofEpi ((CategoryTheory.Limits.kernelCompMono σ.generators.π f).symm ≪≫ CategoryTheory.eqToIso ⋯).hom

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent

Cited by

0 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveCategoryTheory.IsIso