Theorems · Definition · category theory

HomologicalComplex.HasCylinder

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {ι : Type u_2} →
        {c : ComplexShape ι} →
          (K : HomologicalComplex C c) → [∀ (i : ι), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (K.X i)] → Prop

Given a homological complex K, this is the property that the morphism K ⟶ K ⊞ K induced by 𝟙 K and -𝟙 K has a cofiber, which allows to define K.cylinder as this cofiber.

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

27 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct