Theorems · Definition · algebraic topology

SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSucc

{X : SSet} →
  {A : X.Subcomplex} →
    {P : A.Pairing} →
      {ι : Type v} →
        [inst : LinearOrder ι] →
          {f : P.RankFunction ι} →
            [P.IsProper] →
              {j : ι} →
                [inst_2 : SuccOrder ι] →
                  [NoMaxOrder ι] →
                    (c : f.Cell j) → SSet.stdSimplex.obj { len := c.dim + 1 } ⟶ (f.filtration (Order.succ j)).toSSet

The morphism Δ[c.dim + 1] ⟶ f.filtration (Order.succ j) given by c : f.Cell j, when f is a rank function for a proper pairing of a subcomplex of a simplicial set.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex

Cited by

9 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderSSet.Subcomplex.Pairing.IsProperSuccOrderNoMaxOrder