Theorems · Theorem · algebraic topology

SSet.N.stdSimplex_map_monoOfLE_yonedaEquiv_symm_simplex

∀ {X : SSet} [inst : X.Nonsingular] {x y : X.N} (h : x ≤ y),
  CategoryTheory.CategoryStruct.comp (SSet.stdSimplex.map (SSet.N.monoOfLE h)) (SSet.yonedaEquiv.symm y.simplex) =
    SSet.yonedaEquiv.symm x.simplex

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Nonsingular
Cited by: 1 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SSet.Nonsingular

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Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functor.mapstatement · cited by 8,698
Equivstatement · cited by 8,337
Oppositestatement · cited by 8,081
Equiv.symmstatement and proof · cited by 3,681
SimplexCategorystatement · cited by 2,204
SSetstatement and proof · cited by 1,283
SSet.stdSimplexstatement and proof · cited by 499
SSet.N.toSstatement and proof · cited by 171

Cited by1

Results whose statement or proof uses this declaration.

SSet.N.stdSimplex_map_monoOfLE_yonedaEquiv_symm_simplex_assocproof · cited by 0