Theorems · Theorem · category theory

SheafOfModules.GeneratingSections.ofEpi_s

∀ {C : Type u'} [inst : CategoryTheory.Category.{v', u'} C] {J : CategoryTheory.GrothendieckTopology C}
  {R : CategoryTheory.Sheaf J RingCat} [inst_1 : CategoryTheory.HasWeakSheafify J AddCommGrpCat]
  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] {M N : SheafOfModules R} (σ : M.GeneratingSections) (p : M ⟶ N)
  [inst_3 : CategoryTheory.Epi p] (i : σ.I), (σ.ofEpi p).s i = SheafOfModules.sectionsMap p (σ.s i)

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators

Cited by

0 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveCategoryTheory.Epi