comp — Mathlib

English

Composing a morphism with the identity morphism yields the original morphism.

Русский

Сочетание морфизма с тождественным морфизмом даёт исходный морфизм.

LaTeX

$$$f.\\text{comp}(\\mathrm{Hom.id}(P)) = f$$$

Lean4

/-- The composition of two homs. -/
@[simps]
noncomputable def comp (f : Hom P' P'') (g : Hom P P') : Hom P P''
    where
  toRingHom := f.toRingHom.comp g.toRingHom
  toRingHom_algebraMap := by simp [← IsScalarTower.algebraMap_apply]
  algebraMap_toRingHom := by simp [← IsScalarTower.algebraMap_apply]

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