Theorems · Definition · algebraic topology

SSet.Subcomplex.Pairing.RankFunction.Cell.index

{X : SSet} →
  {A : X.Subcomplex} →
    {P : A.Pairing} →
      {ι : Type v} →
        [inst : LinearOrder ι] → {f : P.RankFunction ι} → {i : ι} → (c : f.Cell i) → [P.IsProper] → Fin (c.dim + 2)

If c is a cell of a rank function for a proper pairing P of a subcomplex of a simplicial set, this is the index in Fin (c.dim + 2) of the face of the type (I) simplex given by the corresponding type (II) simplex.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex

Cited by

10 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderSSet.Subcomplex.Pairing.IsProper