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Theorems · Theorem · category theory

HomologicalComplex.acyclic_iff

∀ {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), K.Acyclic ↔ ∀ (i : ι), K.ExactAt i
Defined in
Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by
1 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms
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Around this declaration

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HomologicalComplex.acyclic_of_isZero · cited by 0HomologicalComplex.acycli…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtHomologicalComplex.Acyclic · cited by 28HomologicalComplex.AcyclicHomologicalComplex.acyclic_iffCITED BYCITES

Cites6

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Cited by1

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