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Theorems · Theorem · category theory

HomologicalComplex.ExactAt.unop

∀ {ι : Type u_1} {V : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} V] {c : ComplexShape ι}
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {K : HomologicalComplex Vᵒᵖ c} {i : ι},
  K.ExactAt i → K.unop.ExactAt i
Defined in
Mathlib.Algebra.Homology.Opposite
Cited by
4 results in Mathlib
Foundations
Depth 38 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.isSupported_op_iff · cited by 1HomologicalComplex.isSupp…HomologicalComplex.Acyclic.unop · cited by 1Acyclic.unopHomologicalComplex.isSupportedOutside_op_iff · cited by 1HomologicalComplex.isSupp…HomologicalComplex.exactAt_op_iff · cited by 0HomologicalComplex.exactA…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeComplexShape.symm · cited by 83ComplexShape.symmHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtHomologicalComplex.unop · cited by 6HomologicalComplex.unopCategoryTheory.ShortComplex.Exact.unop · cited by 4Exact.unopExactAt.unopCITED BYCITES

Cites9

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Cited by4

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