Theorems · Theorem · category theory
CategoryTheory.ShortComplex.exact_iff_isZero_leftHomology
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(S : CategoryTheory.ShortComplex C) [inst_2 : S.HasHomology], S.Exact ↔ CategoryTheory.Limits.IsZero S.leftHomology- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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- 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.Limits.IsZerostatement · cited by 306
- CategoryTheory.ShortComplex.Exactstatement · cited by 292
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
- CategoryTheory.ShortComplex.leftHomologystatement · cited by 66
- CategoryTheory.ShortComplex.LeftHomologyData.exact_iffproof · cited by 8
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