Theorems · Theorem · category theory
CochainComplex.IsKProjective.homotopyZero_def
∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_3, u_2} C] [inst_1 : CategoryTheory.Abelian C]
{K L : CochainComplex C ℤ} (f : K ⟶ L) (hL : HomologicalComplex.Acyclic L) [inst_2 : K.IsKProjective],
CochainComplex.IsKProjective.homotopyZero f hL = ⋯.some- Cited by
- 0 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- HomologicalComplexstatement · cited by 1,691
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- Nonempty.somestatement and proof · cited by 340
- Homotopystatement · cited by 106
- HomologicalComplex.Acyclicstatement and proof · cited by 28
- CochainComplex.IsKProjectivestatement and proof · cited by 15
- CochainComplex.IsKProjective.homotopyZerostatement · cited by 3
- CochainComplex.IsKProjective.nonempty_homotopy_zerostatement and proof · cited by 1
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