Theorems · Theorem · category theory
CategoryTheory.ShortComplex.Exact.unop
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex Cᵒᵖ}, S.Exact → S.unop.Exact- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Limits.IsZeroproof · cited by 306
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.ShortComplex.LeftHomologyData.Hproof · cited by 236
- CategoryTheory.ShortComplex.HomologyData.leftproof · cited by 130
- CategoryTheory.ShortComplex.HomologyDataproof · cited by 102
- CategoryTheory.ShortComplex.HomologyData.isoproof · cited by 45
- CategoryTheory.ShortComplex.unopstatement · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplex.ExactAt.unopproof · cited by 4
- CategoryTheory.ShortComplex.exact_op_iffproof · cited by 2
- CategoryTheory.ShortComplex.SnakeInput.L₃_exactproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.unopproof · cited by 1