ι_desc — Mathlib

English

The injections from cofan composed with desc recover the data: (s.cofan Δ).inj A followed by s.desc Δ F equals F A.

Русский

Инъекции кокона, затем desc, восстанавливают данные: (s.cofan Δ).inj A; s.desc Δ F = F A.

LaTeX

$$$(s.cofan(\Delta)).inj A \;\circ\; s.desc(\Delta) F = F A$$$

Lean4

@[reassoc (attr := simp)]
theorem ι_desc {Z : C} (Δ : SimplexCategoryᵒᵖ) (F : ∀ A : IndexSet Δ, s.N A.1.unop.len ⟶ Z) (A : IndexSet Δ) :
    (s.cofan Δ).inj A ≫ s.desc Δ F = F A := by apply Cofan.IsColimit.fac

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