Theorems · Definition · algebraic topology
CategoryTheory.SimplicialObject.Splitting.N
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] → {X : CategoryTheory.SimplicialObject C} → X.Splitting → ℕ → CThe "nondegenerate simplices" N n for all n : ℕ.
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.SimplicialObjectstatement and proof · cited by 548
- CategoryTheory.SimplicialObject.Splittingstatement and proof · cited by 59
Cited by99
Results whose statement or proof uses this declaration.
- CategoryTheory.SimplicialObject.Splitting.cofanstatement · cited by 46
- CategoryTheory.SimplicialObject.Splitting.nondegComplexproof · cited by 31
- CategoryTheory.SimplicialObject.Splitting.ιstatement · cited by 21
- CategoryTheory.SimplicialObject.Splitting.πSummandstatement · cited by 17
- CategoryTheory.SimplicialObject.Split.Hom.fstatement · cited by 15
- CategoryTheory.SimplicialObject.Splitting.descstatement and proof · cited by 12
- CategoryTheory.SimplicialObject.Splitting.hom_ext'statement · cited by 5
- CategoryTheory.SimplicialObject.Splitting.mapproof · cited by 5
- CategoryTheory.SimplicialObject.Splitting.ι_descstatement and proof · cited by 5
- CategoryTheory.SimplicialObject.Splitting.cofan_inj_eqstatement · cited by 4
- AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summandstatement and proof · cited by 4
- CategoryTheory.SimplicialObject.Splitting.φstatement · cited by 3