Theorems · Theorem · algebraic geometry

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C}
  [inst_1 : CategoryTheory.HasWeakSheafify J (Type v)] (S : J.MayerVietorisSquare)
  [inst_2 : CategoryTheory.HasWeakSheafify J AddCommGrpCat],
  (S.map
      (CategoryTheory.yoneda.comp
        (((CategoryTheory.Functor.whiskeringRight Cᵒᵖ (Type v) AddCommGrpCat).obj AddCommGrpCat.free).comp
          (CategoryTheory.presheafToSheaf J AddCommGrpCat)))).IsPushout

Defined in

Mathlib.CategoryTheory.Sites.MayerVietorisSquare

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasWeakSheafify