Theorems · Definition · algebraic topology

SSet.horn.IsCompatible.liftOfKanComplex

{X : SSet} →
  {n : ℕ} →
    {i : Fin (n + 2)} →
      {f : (j : Fin (n + 2)) → j ≠ i → (SSet.stdSimplex.obj { len := n } ⟶ X)} →
        [X.KanComplex] → SSet.horn.IsCompatible f → (SSet.stdSimplex.obj { len := n + 1 } ⟶ X)

If X is a Kan complex and f : ∀ (j : Fin (n + 2)) (_ : j ≠ i), Δ[n] ⟶ X is a compatible family of morphisms (which defines a morphism Λ[n + 1, i] ⟶ X), then this is a lifting Δ[n + 1] ⟶ X.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.KanComplex

Cited by

3 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SSet.KanComplex