seagull — Mathlib

English

For i = 0 or 1, the naturality condition holds for δ₂ faces composed with mk.app; i.e., the 2-face maps commute with mk.app via the δ₂ faces.

Русский

Для i = 0 или 1 натуральность выполняется для лицевой карты δ₂, образующейся в mk.app; 2-границы commute

LaTeX

$$$\text{mk_naturality}_{\delta_0i}$ expresses the commutativity of δ₂ with mk.app for i = 0,1.$$

Lean4

/-- This is similar to one of the famous Segal maps, except valued in a product rather than a
pullback. -/
noncomputable def seagull (C : Type u) [Category C] :
    (nerveFunctor₂.obj (Cat.of C)).obj (op ⦋2⦌₂) ⟶
      (nerveFunctor₂.obj (Cat.of C)).obj (op ⦋1⦌₂) ⨯ (nerveFunctor₂.obj (Cat.of C)).obj (op ⦋1⦌₂) :=
  prod.lift ((nerveFunctor₂.obj (Cat.of C)).map (.op δ2₂)) ((nerveFunctor₂.obj (Cat.of C)).map (.op δ0₂))

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