Theorems · Definition · algebraic topology
SSet.degenerate
(X : SSet) → (n : ℕ) → Set (X.obj (Opposite.op { len := n }))An n-simplex of a simplicial set X is degenerate if it is in the range
of X.map f.op for some morphism f : [n] ⟶ [m] with m < n.
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- Quiver.Hom.opproof · cited by 1,948
- SSetstatement and proof · cited by 1,283
Cited by32
Results whose statement or proof uses this declaration.
- SSet.nonDegenerateproof · cited by 106
- SSet.nonDegenerate_iff_of_monoproof · cited by 6
- SSet.degenerate_eq_univ_of_hasDimensionLTstatement · cited by 6
- SSet.Subcomplex.mem_degenerate_iffstatement and proof · cited by 5
- SSet.degenerate_eq_iUnion_range_σstatement and proof · cited by 4
- SSet.Subcomplex.mem_nonDegenerate_iffproof · cited by 4
- PartialOrder.mem_nerve_nonDegenerate_iff_strictMonoproof · cited by 3
- SSet.degenerate_app_applystatement and proof · cited by 3
- SSet.hasDimensionLT_of_epiproof · cited by 2
- SSet.mem_degenerate_iffstatement and proof · cited by 2
- SSet.mem_degenerate_iff_notMem_nonDegeneratestatement and proof · cited by 2
- SSet.mem_nonDegenerate_iff_notMem_degeneratestatement · cited by 2