map_comp — Mathlib

English

The composed map map Q g hy, when composed with algebraMap_R_S, equals the composition algebraMap_P_Q ∘ g; i.e., the diagram commutes.

Русский

Сложение map Q g hy с algebraMap_R_S эквивалентно композиции algebraMap_P_Q ∘ g; диаграмма коммутирует.

LaTeX

$$$ (map\\ Q\\ g\\ hy).\\text{\\.}\\text{comp} (\\mathrm{algebraMap}_{R,S}) = (\\mathrm{algebraMap}_{P,Q}).\\circ g. $$$

Lean4

@[simp]
theorem map_comp : (map Q g hy).comp (algebraMap R S) = (algebraMap P Q).comp g :=
  lift_comp fun y => map_units _ ⟨g y, hy y.2⟩

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