Theorems · Definition · category theory
ChainComplex.alternatingConstHomotopyEquiv
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
[inst_2 : CategoryTheory.Limits.HasZeroObject C] →
(X : C) → HomotopyEquiv (ChainComplex.alternatingConst.obj X) ((ChainComplex.single₀ C).obj X)alternatingConst.obj X is homotopy equivalent to the chain
complex (single₀ C).obj X.
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- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Iso.symmproof · cited by 993
- ComplexShape.downstatement · cited by 605
- ChainComplexstatement · cited by 350
- CategoryTheory.Iso.appproof · cited by 253
- ChainComplex.single₀statement · cited by 69
- HomotopyEquivstatement · cited by 27
- HomotopyEquiv.transproof · cited by 4
- HomotopyEquiv.ofIsoproof · cited by 3
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