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Theorems · Theorem · category theory

CochainComplex.IsKProjective.nonempty_homotopy_zero

∀ {C : Type u_1} {inst : CategoryTheory.Category.{v_1, u_1} C} {inst_1 : CategoryTheory.Abelian C}
  {K : CochainComplex C ℤ} [self : K.IsKProjective] {L : CochainComplex C ℤ} (f : K ⟶ L),
  HomologicalComplex.Acyclic L → Nonempty (Homotopy f 0)
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.KProjective
Cited by
1 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CochainComplex.IsKProjective
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Around this declaration

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CochainComplex.IsKProjective.homotopyZero_def · cited by 0IsKProjective.homotopyZer…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianHomologicalComplex · cited by 1691HomologicalComplexComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomotopy · cited by 106HomotopyHomologicalComplex.Acyclic · cited by 28HomologicalComplex.AcyclicCochainComplex.IsKProjective · cited by 15CochainComplex.IsKProject…IsKProjective.nonempty_homoto…CITED BYCITES

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