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Theorems · Theorem · category theory

HomologicalComplex.exactAt_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) (i : ι), K.ExactAt i ↔ (K.sc i).Exact
Defined in
Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by
3 results in Mathlib
Foundations
Depth 24 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.

HomologicalComplex.exactAt_iff_isZero_homology · cited by 13HomologicalComplex.exactA…HomologicalComplex.ExactAt.of_iso · cited by 2ExactAt.of_isoisZero_Ext_succ_of_projective · cited by 1isZero_Ext_succ_of_projec…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeCategoryTheory.ShortComplex.Exact · cited by 292ShortComplex.ExactHomologicalComplex.sc · cited by 205HomologicalComplex.scHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtHomologicalComplex.exactAt_iffCITED BYCITES

Cites7

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Cited by3

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