Theorems · Theorem · category theory

HomologicalComplex.ExactAt.of_iso

∀ {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 → ∀ {L : HomologicalComplex C c} (e : K ≅ L), L.ExactAt i

Defined in: Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by: 2 results in Mathlib
Foundations: Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms

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

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Isostatement and proof · cited by 3,963
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
HomologicalComplexstatement and proof · cited by 1,691
ComplexShapestatement and proof · cited by 1,684
CategoryTheory.Functor.mapIsoproof · cited by 224
HomologicalComplex.shortComplexFunctorproof · cited by 72
HomologicalComplex.ExactAtstatement and proof · cited by 44
CategoryTheory.ShortComplex.exact_of_isoproof · cited by 18
HomologicalComplex.exactAt_iffproof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

HomologicalComplex.isSupported_of_isoproof · cited by 2
AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpaceproof · cited by 1