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Theorems · Theorem · algebraic topology

SSet.stdSimplex.face_eq_ofSimplex

∀ {n : ℕ} (S : Finset (Fin (n + 1))) (m : ℕ) (e : Fin (m + 1) ≃o ↥S),
  SSet.stdSimplex.face S =
    SSet.Subcomplex.ofSimplex
      (SSet.stdSimplex.objMk ((OrderHom.Subtype.val fun x => x ∈ S).comp e.toOrderEmbedding.toOrderHom))
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
Cited by
3 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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SSet.stdSimplex.face_singleton_compl · cited by 6stdSimplex.face_singleton…SSet.stdSimplex.ofSimplex_yonedaEquiv_δ · cited by 1stdSimplex.ofSimplex_yone…SSet.stdSimplex.face_nonDegenerateEquiv' · cited by 1stdSimplex.face_nonDegene…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Functor.obj · cited by 19642Functor.objFinset · cited by 13712FinsetCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homOpposite.unop · cited by 2231Opposite.unopSimplexCategory · cited by 2204SimplexCategoryle_antisymm · cited by 2068le_antisymmQuiver.Hom.op · cited by 1948Hom.opSSet · cited by 1283SSetOrderHom · cited by 934OrderHomOrderIso · cited by 874OrderIsoSimplexCategory.len · cited by 542SimplexCategory.lenSSet.stdSimplex · cited by 499SSet.stdSimplexstdSimplex.face_eq_ofSimplexCITED BYCITES

Cites36

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Cited by3

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