Theorems · Theorem · category theory
CategoryTheory.ShortComplex.abLeftHomologyData_H_coe
∀ (S : CategoryTheory.ShortComplex Ab), ↑S.abLeftHomologyData.H = (↥(AddCommGrpCat.Hom.hom S.g).ker ⧸ S.abToCycles.range)
- Defined in
- Mathlib.Algebra.Homology.ShortComplex.Ab
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement · cited by 658
- AddCommGrpCat.carrierstatement and proof · cited by 407
- CategoryTheory.ShortComplex.LeftHomologyData.Hstatement and proof · cited by 236
- Abstatement and proof · cited by 198
- AddMonoidHom.kerstatement · cited by 158
- AddMonoidHom.rangestatement · cited by 142
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