Theorems · Definition · category theory

HomologicalComplex.prepathObject

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

The pre-path object of a homological complex that is given by HomologicalComplex.pathObject.

Defined in

Mathlib.Algebra.Homology.Precylinder

Cited by

4 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveDecidableRelCategoryTheory.Limits.HasBinaryBiproductHomologicalComplex.HasPathObject