Theorems · Theorem · algebraic topology

SSet.horn.IsCompatible.lift_comp_assoc

∀ {X : SSet} {n : ℕ} {i : Fin (n + 2)} {f : (j : Fin (n + 2)) → j ≠ i → (SSet.stdSimplex.obj { len := n } ⟶ X)}
  (hf : SSet.horn.IsCompatible f) {Y : SSet} (p : X ⟶ Y) [inst : HomotopicalAlgebra.Fibration p]
  (b : SSet.stdSimplex.obj { len := n + 1 } ⟶ Y)
  (comm :
    ∀ (j : Fin (n + 2)) (hj : j ≠ i),
      CategoryTheory.CategoryStruct.comp (f j hj) p = CategoryTheory.CategoryStruct.comp (SSet.stdSimplex.δ j) b)
  {Z : SSet} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (hf.lift p b comm) (CategoryTheory.CategoryStruct.comp p h) =
    CategoryTheory.CategoryStruct.comp b h

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

HomotopicalAlgebra.Fibration