toUnder_comp — Mathlib

English

Composition of algebra homomorphisms corresponds to composition in Under via toUnder.

Русский

Сложение алгебраических гомоморфизмов соответствует композиции в Under через toUnder.

LaTeX

$$$ (g \circ f).toUnder = f.toUnder \; \circ \; g.toUnder $$$

Lean4

@[simp]
theorem toUnder_comp {A B C : Type u} [CommRing A] [CommRing B] [CommRing C] [Algebra R A] [Algebra R B] [Algebra R C]
    (f : A →ₐ[R] B) (g : B →ₐ[R] C) : (g.comp f).toUnder = f.toUnder ≫ g.toUnder :=
  rfl

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