comp — Mathlib

English

The composition of two nonunital algebra homomorphisms is again a nonunital algebra homomorphism.

Русский

Состав двух неполунальных алгебра-гомоморфизмов снова является неполунальным алгебра-гомоморфизмом.

LaTeX

$$$\text{If } f: B \to C \text{ and } g: A \to B \text{ are nonunital algebra homomorphisms, then } f \circ g: A \to C \text{ is a nonunital algebra homomorphism.}$$$

Lean4

/-- The composition of morphisms is a morphism. -/
def comp (f : B →ₛₙₐ[ψ] C) (g : A →ₛₙₐ[φ] B) [κ : MonoidHom.CompTriple φ ψ χ] : A →ₛₙₐ[χ] C :=
  { (f : B →ₙ* C).comp (g : A →ₙ* B), (f : B →ₑ+[ψ] C).comp (g : A →ₑ+[φ] B) with }

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