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Theorems · Theorem · category theory

HomologicalComplex.ExactAt.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} {i : ι},
  CategoryTheory.Limits.IsZero (K.X i) → K.ExactAt i
Defined in
Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by
1 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.exactAt_chainComplex_of_hasDimensionLT · cited by 1SSet.exactAt_chainComplex…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex.X · cited by 1839HomologicalComplex.XHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroHomologicalComplex.sc · cited by 205HomologicalComplex.scHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtCategoryTheory.ShortComplex.exact_of_isZero_X₂ · cited by 8ShortComplex.exact_of_isZ…ExactAt.of_isZeroCITED BYCITES

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Cited by1

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