Theorems · Definition · category theory
HomologicalComplex.unop
{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] → HomologicalComplex Vᵒᵖ c → HomologicalComplex V c.symmSends a complex X with objects in Vᵒᵖ to the corresponding complex with objects in V.
- Defined in
- Mathlib.Algebra.Homology.Opposite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Opposite.unopproof · cited by 2,231
- HomologicalComplex.Xproof · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- Quiver.Hom.unopproof · cited by 903
- HomologicalComplex.dproof · cited by 598
- ComplexShape.Relproof · cited by 518
- ComplexShape.symmstatement and proof · cited by 83
Cited by11
Results whose statement or proof uses this declaration.
- HomologicalComplex.truncLEproof · cited by 19
- HomologicalComplex.truncLE'proof · cited by 15
- HomologicalComplex.unopFunctorproof · cited by 14
- ChainComplex.linearYonedaObjproof · cited by 6
- HomologicalComplex.ExactAt.unopstatement · cited by 4
- HomologicalComplex.unop_dstatement and proof · cited by 1
- HomologicalComplex.Acyclic.unopstatement · cited by 1
- HomologicalComplex.unopFunctor_map_fstatement · cited by 0
- HomologicalComplex.unopFunctor_objstatement · cited by 0
- HomologicalComplex.unop_Xstatement and proof · cited by 0
- HomologicalComplex.homologyUnopstatement and proof · cited by 0