Theorems · Theorem · algebraic topology

SSet.Truncated.spine_map_subinterval

∀ {n : ℕ} (X : SSet.Truncated (n + 1)) (m : ℕ) (hₘ : m ≤ n + 1) (j l : ℕ) (h : j + l ≤ m)
  (Δ : X.obj (Opposite.op { obj := { len := m }, property := hₘ })),
  X.spine l ⋯
      ((CategoryTheory.ConcreteCategory.hom
          (X.map (SimplexCategory.Truncated.Hom.tr (SimplexCategory.subinterval j l h) ⋯ hₘ).op))
        Δ) =
    (X.spine m hₘ Δ).interval j l h

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Path

Cited by

2 results in Mathlib

Foundations

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