Theorems · Definition · algebraic topology
SSet.splitting
(X : SSet) → CategoryTheory.SimplicialObject.Splitting X
The canonical splitting of a simplicial set that is given by the nondegenerate simplices.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oppositeproof · cited by 8,081
- Set.Elemproof · cited by 7,166
- SimplexCategoryproof · cited by 2,204
- SSetstatement and proof · cited by 1,283
- CategoryTheory.Limits.IsColimitproof · cited by 773
- TypeCat.ofHomproof · cited by 389
- Nonempty.someproof · cited by 340
- SSet.nonDegenerateproof · cited by 106
- CategoryTheory.SimplicialObject.Splittingstatement · cited by 59
- CategoryTheory.SimplicialObject.Splitting.cofan'proof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- SSet.normalizedChainComplexproof · cited by 29
- SSet.toNormalizedChainComplexproof · cited by 20
- SSet.fromNormalizedChainComplexproof · cited by 12
- SSet.toNormalizedChainComplex_fromNormalizedChainComplexproof · cited by 2
- SSet.fromNormalizedChainComplex_toNormalizedChainComplexproof · cited by 2
- SSet.homotopyEquivNormalizedChainComplexproof · cited by 2
- SSet.PInfty_toNormalizedChainComplexproof · cited by 2
- SSet.splitting_Nstatement and proof · cited by 0
- SSet.splitting_ιstatement and proof · cited by 0