of_counit — Mathlib

English

For any X that carries a coalgebra structure over R, the counit on the CoalgCat object obtained via of X equals the original counit on X.

Русский

Для X сcoalgebra над R, кокнуция на объекте CoalgCat, полученном через of X, равна исходной кокнюйте на X.

LaTeX

$$$\\operatorname{Coalgebra}.counit( A := \\text{of } R X) = \\operatorname{Coalgebra}.counit( R := R)( A := X)$$$

Lean4

@[simp]
theorem of_counit {X : Type v} [AddCommGroup X] [Module R X] [Coalgebra R X] :
    Coalgebra.counit (A := of R X) = Coalgebra.counit (R := R) (A := X) :=
  rfl

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