Theorems · Definition · algebraic topology
SSet.N.monoOfLE
{X : SSet} → [X.Nonsingular] → {x y : X.N} → x ≤ y → ({ len := x.dim } ⟶ { len := y.dim })Given an inequality x ≤ y between nondegenerate simplices of a
nonsingular simplicial set X, this is the corresponding morphism
⦋x.dim⦌ ⟶ ⦋y.dim⦌ in the simplex category.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SSet.Nonsingular
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.
- Quiver.Homstatement · cited by 32,603
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.N.toSstatement · cited by 171
- SSet.S.dimstatement · cited by 162
- SSet.Nstatement and proof · cited by 70
- SSet.Nonsingularstatement and proof · cited by 22
Cited by10
Results whose statement or proof uses this declaration.
- SSet.N.toSemiSimplexCategoryproof · cited by 3
- SSet.N.map_monoOfLEstatement · cited by 3
- SSet.N.monoOfLE_compstatement and proof · cited by 1
- SSet.N.stdSimplex_map_monoOfLE_yonedaEquiv_symm_simplexstatement and proof · cited by 1
- SSet.N.toSemiSimplexCategory_mapstatement · cited by 0
- SSet.N.monoOfLE_comp_assocstatement and proof · cited by 0
- SSet.N.monoOfLE_eq_iffstatement and proof · cited by 0
- SSet.N.monoOfLE_reflstatement · cited by 0
- SSet.N.monoOfLE.congr_simpstatement and proof · cited by 0
- SSet.N.stdSimplex_map_monoOfLE_yonedaEquiv_symm_simplex_assocstatement and proof · cited by 0