Theorems · Definition · category theory

HomologicalComplex.cylinder.inlX

{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) →
            [inst_2 : DecidableRel c.Rel] →
              [inst_3 : ∀ (i : ι), CategoryTheory.Limits.HasBinaryBiproduct (K.X i) (K.X i)] →
                [inst_4 : K.HasCylinder] → (i j : ι) → c.Rel j i → (K.X i ⟶ K.cylinder.X j)

The left inclusion K.X i ⟶ K.cylinder.X j when c.Rel j i.

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveDecidableRelCategoryTheory.Limits.HasBinaryBiproductHomologicalComplex.HasCylinder