Theorems · Theorem · category theory

SheafOfModules.GeneratingSections.opEpi_comp

∀ {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 P : SheafOfModules R} (σ : M.GeneratingSections) (p : M ⟶ N)
  (q : N ⟶ P) [inst_3 : CategoryTheory.Epi p] [inst_4 : CategoryTheory.Epi q],
  σ.ofEpi (CategoryTheory.CategoryStruct.comp p q) = (σ.ofEpi p).ofEpi q

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.EpiCategoryTheory.Epi