ofIsStrictSegal — Mathlib

English

Yoneda equivalence interacts coherently with Subcomplex inclusions and morphisms.

Русский

Янида-эквив относится к подпслоям и морфизмам согласованно.

LaTeX

$$yonedaEquiv_coe {A : X.Subcomplex} {n} (f : stdSimplex.obj n ⟶ A) : …$$

Lean4

/-- Given `IsStrictSegal X`, a choice of inverse to `spine X m` for all
`m ≤ n + 1` determines an inhabitant of `StrictSegal X`. -/
noncomputable def ofIsStrictSegal [IsStrictSegal X] : StrictSegal X
    where
  spineToSimplex m h := Equiv.ofBijective (X.spine m) (IsStrictSegal.segal m h) |>.invFun
  spine_spineToSimplex m _ := funext <| Equiv.ofBijective (X.spine m) _ |>.right_inv
  spineToSimplex_spine m _ := funext <| Equiv.ofBijective (X.spine m) _ |>.left_inv

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