Theorems · Definition · algebraic topology
SSet.chainComplex
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Limits.HasCoproducts C] → [inst_2 : CategoryTheory.Preadditive C] → SSet → C → ChainComplex C ℕThe (simplicial) chain complex of a simplicial set X with
coefficients in R : C. Its homology is the simplicial homology
of X.
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.objproof · cited by 19,642
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SSetstatement and proof · cited by 1,283
- ChainComplexstatement · cited by 350
- CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
- SSet.chainComplexFunctorproof · cited by 3
Cited by62
Results whose statement or proof uses this declaration.
- SSet.toNormalizedChainComplexstatement · cited by 20
- SSet.ιChainComplexstatement · cited by 20
- SSet.homologyproof · cited by 13
- SSet.fromNormalizedChainComplexstatement · cited by 12
- SSet.homologyData₀statement and proof · cited by 8
- SSet.chainComplexMapstatement · cited by 8
- SSet.π₀.fromChainComplexXZerostatement · cited by 7
- SSet.homology₀Isoproof · cited by 3
- SSet.π₀.comp_fromChainComplexXZerostatement · cited by 3
- SSet.fromNormalizedChainComplex_toNormalizedChainComplexstatement · cited by 2
- SSet.homotopyEquivNormalizedChainComplexstatement · cited by 2
- SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_fstatement · cited by 2