Theorems · Theorem · category theory
CategoryTheory.ShortComplex.Exact.hasHomology
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C}, S.Exact → S.HasHomology- Cited by
- 12 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.ShortComplex.HasHomologystatement · cited by 253
- CategoryTheory.ShortComplex.HasHomology.mk'proof · cited by 9
- CategoryTheory.ShortComplex.Exact.conditionproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Exact.mapproof · cited by 11
- CategoryTheory.ShortComplex.Exact.mono_gproof · cited by 10
- CategoryTheory.ShortComplex.exact_iff_monoproof · cited by 8
- CategoryTheory.ShortComplex.exact_iff_epiproof · cited by 8
- CategoryTheory.ShortComplex.Exact.epi_fproof · cited by 8
- CategoryTheory.ShortComplex.Exact.mono_g'proof · cited by 5
- CategoryTheory.ShortComplex.Exact.epi_f'proof · cited by 5
- CategoryTheory.ShortComplex.Exact.map_of_preservesLeftHomologyOfproof · cited by 1
- CategoryTheory.ShortComplex.Exact.comp_eq_zeroproof · cited by 1
- CategoryTheory.ShortComplex.Exact.map_of_preservesRightHomologyOfproof · cited by 0
- CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer'proof · cited by 0
- CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer'proof · cited by 0