Theorems · Theorem · category theory
HomologicalComplex.acyclic_of_isZero
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{ι : Type u_2} {c : ComplexShape ι} (K : HomologicalComplex C c), CategoryTheory.Limits.IsZero K → K.Acyclic- Cited by
- 0 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.Limits.IsZerostatement and proof · cited by 306
- HomologicalComplex.scproof · cited by 205
- HomologicalComplex.evalproof · cited by 84
- HomologicalComplex.Acyclicstatement · cited by 28
- CategoryTheory.Functor.map_isZeroproof · cited by 16
- CategoryTheory.ShortComplex.exact_of_isZero_X₂proof · cited by 8
- HomologicalComplex.acyclic_iffproof · cited by 1
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