Theorems · Theorem · category theory
HomologicalComplex.Acyclic.op
∀ {ι : Type u_1} {V : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} V] {c : ComplexShape ι}
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {K : HomologicalComplex V c}, K.Acyclic → K.op.Acyclic- Defined in
- Mathlib.Algebra.Homology.Opposite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.symmstatement · cited by 83
- HomologicalComplex.opstatement · cited by 50
- HomologicalComplex.Acyclicstatement and proof · cited by 28
- HomologicalComplex.ExactAt.opproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- HomologicalComplex.acyclic_op_iffproof · cited by 1