subsingleton_to_ring — Mathlib

English

There is a Subsingleton of coalgebra homomorphisms from A to R: all such maps are equal.

Русский

Существует единичность между коалгоморфизмами A → R: все такие отображения равны.

LaTeX

$$$\text{Subsingleton}(A \to_{c} R)$$$

Lean4

instance subsingleton_to_ring : Subsingleton (A →ₗc[R] R) :=
  ⟨fun f g =>
    CoalgHom.ext fun x => by
      have hf := CoalgHomClass.counit_comp_apply f x
      have hg := CoalgHomClass.counit_comp_apply g x
      simp_all only [CommSemiring.counit_apply]⟩

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