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Theorems · Theorem · category theory

HomologicalComplex.IsSupportedOutside.exactAt

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {K : HomologicalComplex C c'} {e : c.Embedding c'}, K.IsSupportedOutside e → ∀ (i : ι), K.ExactAt (e.f i)
Defined in
Mathlib.Algebra.Homology.Embedding.IsSupported
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.acyclic_truncGE_iff_isSupportedOutside · cited by 3HomologicalComplex.acycli…ComplexShape.Embedding.AreComplementary.isSupportedOutside₁_iff · cited by 2AreComplementary.isSuppor…HomologicalComplex.isSupportedOutside_op_iff · cited by 1HomologicalComplex.isSupp…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeComplexShape.Embedding · cited by 337ComplexShape.EmbeddingComplexShape.Embedding.f · cited by 251Embedding.fHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtHomologicalComplex.IsSupportedOutside · cited by 8HomologicalComplex.IsSupp…IsSupportedOutside.exactAtCITED BYCITES

Cites8

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Cited by3

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