commuting — Mathlib

English

As in ForgetCreatesColimits.commuting, the relation between T.map and lambda holds for each j, matching the D-algebra structure after forgetting; explicitly: (T.map c.ι.app j) ≫ lambda c t = (D.obj j).a ≫ c.ι.app j.

Русский

Как в ForgetCreatesColimits.commuting, равенство между отображением T и лямбдой сохраняется для каждого j: (T.map c.ι.app j) ≫ lambda c t = (D.obj j).a ≫ c.ι.app j.

LaTeX

$$$ (T : C ⥤ C).map (c.ι.app j) ≫ \lambda c t = (D.obj j).a ≫ c.ι.app j $$$

Lean4

/-- (Impl) The key property defining the map `λ : TL ⟶ L`. -/
theorem commuting (j : J) : (T : C ⥤ C).map (c.ι.app j) ≫ lambda c t = (D.obj j).a ≫ c.ι.app j :=
  (isColimitOfPreserves _ t).fac (newCocone c) j

Похожие утверждения