comp — Mathlib

English

The first projection from a product is a non-unital star-algebra homomorphism.

Русский

Первая проекция из произведения является ненулевым⋆-алгебра-гомоморфизмом.

LaTeX

$$$\mathrm{fst}: A \times B \to⋆ₙₐ[R] A$$$

Lean4

/-- The composition of ⋆-algebra homomorphisms, as a ⋆-algebra homomorphism. -/
def comp (f : B →⋆ₐ[R] C) (g : A →⋆ₐ[R] B) : A →⋆ₐ[R] C :=
  { f.toAlgHom.comp g.toAlgHom with
    map_star' := by
      simp only [map_star, AlgHom.toFun_eq_coe, AlgHom.coe_comp, coe_toAlgHom, Function.comp_apply, forall_const] }

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