Theorems · Theorem · algebraic topology

SSet.Subcomplex.liftPath_vertex_coe

∀ {X : SSet} (A : X.Subcomplex) {n : ℕ} (p : X.Path n)
  (hp₀ : ∀ (j : Fin (n + 1)), p.vertex j ∈ A.obj (Opposite.op { len := 0 }))
  (hp₁ : ∀ (j : Fin n), p.arrow j ∈ A.obj (Opposite.op { len := 1 })) (j : Fin (n + 1)),
  ↑((A.liftPath p hp₀ hp₁).vertex j) = p.vertex j

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Path

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound