id — Mathlib · SciLib

English

Two coalgebra endomorphisms are equal if their values on 1 agree

Русский

Два эндоморфизма коалгебры равны, если их значения на 1 совпадают

LaTeX

$$$$ f(1) = g(1) \Rightarrow f = g $$$$

Lean4

/-- Identity map as a `CoalgHom`. -/
@[simps!]
protected def id : A →ₗc[R] A :=
  { LinearMap.id with
    counit_comp := by ext; rfl
    map_comp_comul := by simp only [map_id, LinearMap.id_comp, LinearMap.comp_id] }

Похожие утверждения