comul_eq_lift — Mathlib

English

There is an equivalence between functors Cat.chosenTerminal ⥤ C and objects of C.

Русский

Существует эквиваленция между функторaми Cat.chosenTerminal ⥤ C и объектами C.

LaTeX

$$$$\mathrm{fromChosenTerminalEquiv}: \mathrm{Cat.chosenTerminal} \boxtimes C \simeq C.$$$$

Lean4

@[simp]
theorem comul_eq_lift (A : C) [ComonObj A] : Δ[A] = lift (𝟙 _) (𝟙 _) :=
  by
  ext
  · simpa using comul_counit A =≫ fst _ _
  · simpa using counit_comul A =≫ snd _ _

Похожие утверждения