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Theorems · Theorem · algebraic topology

SSet.N.existsUnique_of_le

∀ {X : SSet} [X.Nonsingular] {x y : X.N},
  x ≤ y → ∃! f, CategoryTheory.Mono f ∧ (CategoryTheory.ConcreteCategory.hom (X.map f.op)) y.simplex = x.simplex
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Nonsingular
Cited by
2 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SSet.Nonsingular
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.N.map_monoOfLE · cited by 3N.map_monoOfLESSet.N.monoOfLE_eq_iff · cited by 0N.monoOfLE_eq_iffDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opTypeCat.Fun · cited by 1307TypeCat.FunSSet · cited by 1283SSetCategoryTheory.Mono · cited by 893CategoryTheory.MonoExistsUnique · cited by 268ExistsUniqueSSet.N.toS · cited by 171N.toSSSet.S.dim · cited by 162S.dimSSet.S.simplex · cited by 111S.simplexN.existsUnique_of_leCITED BYCITES

Cites21

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Cited by2

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