Theorems · Theorem · algebraic topology

SSet.horn.IsCompatible.exists_lift_of_kanComplex

∀ {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 →
    ∃ φ, ∀ (j : Fin (n + 2)) (hj : j ≠ i), CategoryTheory.CategoryStruct.comp (SSet.stdSimplex.δ j) φ = f j hj

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.KanComplex

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SSet.KanComplex