Theorems · Theorem · category theory
CategoryTheory.ShortComplex.exact_iff_mono_fromOpcycles
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
(S : CategoryTheory.ShortComplex C) [inst_2 : S.HasHomology], S.Exact ↔ CategoryTheory.Mono S.fromOpcycles- Cited by
- 2 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.Exactstatement · cited by 292
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.opcyclesstatement · cited by 192
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
- CategoryTheory.ShortComplex.fromOpcyclesstatement · cited by 38
- CategoryTheory.ShortComplex.RightHomologyData.exact_iff_mono_g'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.ShortComplex.exact_iff_mono_cokernel_descproof · cited by 1