Theorems · Definition · algebraic topology
SSet.nonDegenerate
(X : SSet) → (n : ℕ) → Set (X.obj (Opposite.op { len := n }))The set of n-dimensional non-degenerate simplices in a simplicial
set X is the complement of X.degenerate n.
- Cited by
- 106 results in Mathlib
- Foundations
- Depth 33 from the axioms, rests on 294 definitions · uses propext, 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.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Compl.complproof · cited by 2,925
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.degenerateproof · cited by 29
Cited by136
Results whose statement or proof uses this declaration.
- SSet.N.mkstatement and proof · cited by 19
- SSet.skeletonproof · cited by 11
- SSet.N.nonDegeneratestatement · cited by 11
- SSet.dim_lt_of_nonDegeneratestatement and proof · cited by 7
- SSet.Subcomplex.le_iff_contains_nonDegeneratestatement and proof · cited by 7
- SSet.Subcomplex.N.mkstatement and proof · cited by 6
- SSet.nonDegenerate_iff_of_monostatement · cited by 6
- SSet.splittingproof · cited by 5
- SSet.Nonsingular.mono'statement and proof · cited by 5
- SSet.stdSimplex.nonDegenerateEquiv'statement and proof · cited by 5
- SSet.exists_nonDegeneratestatement and proof · cited by 4
- SSet.mem_skeletonproof · cited by 4