Theorems · Definition · category theory

HomologicalComplex.pathObject

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {α : Type u_2} →
        {c : ComplexShape α} →
          (K : HomologicalComplex C c) →
            [DecidableRel c.Rel] →
              [inst_3 : ∀ (i : α), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (K.X i)] →
                [K.HasPathObject] → HomologicalComplex C c.symm.symm

The path object of a homological complex is defined here by dualizing the cylinder object of K.op.

Defined in

Mathlib.Algebra.Homology.HomotopyFiber

Cited by

23 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveDecidableRelCategoryTheory.Limits.HasBinaryBiproductHomologicalComplex.HasPathObject