underlyingIso_top_hom — Mathlib

English

The hom component of the underlying isomorphism for identity 1_B equals the top-arrow of the top subobject of B.

Русский

Гомоморфизм компонентаUnderlyingIso(1_B) равен верхнему стрелке верхнего подпредмета B.

LaTeX

$$$(\text{underlyingIso } (1_B)).{\text{hom}} = (\top : \operatorname{Subobject} B).\arrow$$$

Lean4

theorem underlyingIso_top_hom {B : C} : (underlyingIso (𝟙 B)).hom = (⊤ : Subobject B).arrow :=
  by
  convert underlyingIso_hom_comp_eq_mk (𝟙 B)
  simp only [comp_id]

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