Theorems · Definition · category theory
CochainComplex.opEquivalence
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (CochainComplex C ℤ)ᵒᵖ ≌ CochainComplex Cᵒᵖ ℤThe equivalence of categories (CochainComplex C ℤ)ᵒᵖ ≌ CochainComplex Cᵒᵖ ℤ.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 57 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 and proof · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- ComplexShape.upstatement and proof · cited by 1,123
- CochainComplexstatement · cited by 1,016
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Equivalence.transproof · cited by 57
- HomologicalComplex.opEquivalenceproof · cited by 4
- ChainComplex.cochainComplexEquivalenceproof · cited by 0
Cited by9
Results whose statement or proof uses this declaration.
- CochainComplex.homotopyUnopstatement and proof · cited by 2
- CochainComplex.isKProjective_of_opstatement and proof · cited by 1
- CochainComplex.homotopyOpstatement · cited by 1
- CochainComplex.exactAt_opstatement and proof · cited by 1
- CochainComplex.acyclic_opstatement · cited by 1
- CochainComplex.isKProjective_of_projectiveproof · cited by 0
- CochainComplex.homotopyOpEquivstatement and proof · cited by 0
- CochainComplex.homotopyOp_hom_eqstatement · cited by 0
- CochainComplex.homotopyUnop_hom_eqstatement and proof · cited by 0