Theorems · Definition · algebraic topology
SSet.homology
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Limits.HasCoproducts C] →
[inst_2 : CategoryTheory.Preadditive C] → SSet → C → [CategoryTheory.CategoryWithHomology C] → ℕ → CThe simplicial homology with coefficients in R : C in degree n
of a simplicial set X.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 79 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.Preadditivestatement and proof · cited by 3,309
- SSetstatement and proof · cited by 1,283
- HomologicalComplex.homologyproof · cited by 209
- CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
- CategoryTheory.CategoryWithHomologystatement and proof · cited by 116
- SSet.chainComplexproof · cited by 46
Cited by17
Results whose statement or proof uses this declaration.
- SSet.homologyMapstatement · cited by 9
- SSet.homology₀Isostatement · cited by 3
- SSet.homologyFunctorproof · cited by 2
- SSet.homology₀εstatement · cited by 2
- CategoryTheory.SimplicialObject.Homotopy.congr_sSetHomologyMapstatement · cited by 2
- SSet.homologyMap_compstatement · cited by 1
- SSet.liftCycles_ιChainComplex_homologyπ_homology₀Iso_homstatement · cited by 1
- SSet.liftCycles_ιChainComplex_homologyπ_homology₀Iso_hom_assocstatement · cited by 1
- SSet.Homotopy.congr_homologyMapstatement · cited by 1
- SSet.homologyFunctor_mapstatement · cited by 0
- SSet.homologyFunctor_objstatement · cited by 0