Theorems · Theorem · category theory

HomologicalComplex.isSeparator_coproduct_separatingFamily

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {ι : Type w} (c : ComplexShape ι) [c.HasNoLoop]
  [inst_2 : CategoryTheory.Limits.HasCoproductsOfShape ι C] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : CategoryTheory.Limits.HasZeroObject C] {X : C},
  CategoryTheory.IsSeparator X →
    CategoryTheory.IsSeparator (∐ fun i => HomologicalComplex.separatingFamily c (fun x => X) (PUnit.unit, i))

Defined in

Mathlib.CategoryTheory.Generator.HomologicalComplex

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryComplexShape.HasNoLoopCategoryTheory.Limits.HasCoproductsOfShapeCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject