Theorems · Theorem · category theory
HomotopyCategory.plus_quotient_obj_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
(K : CochainComplex C ℤ),
HomotopyCategory.plus C ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K) ↔ CochainComplex.plus C K- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement · cited by 1,691
- ComplexShape.upstatement and proof · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomotopyCategorystatement · cited by 132
- HomotopyCategory.quotientstatement and proof · cited by 109
- CategoryTheory.Quotient.asproof · cited by 47
- CochainComplex.plusstatement and proof · cited by 24
- HomotopyCategory.plusstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- HomotopyCategory.Plus.quotient_obj_surjectiveproof · cited by 0