map_id_comp — Mathlib

English

The map coprod.map (id W) (f ≫ g) equals the composite coprod.map id W f ≫ coprod.map id W g under suitable coproduct hypotheses.

Русский

Копрод. map (id W) (f ≫ g) эквивалентно compose (map id f) (map id g).

LaTeX

$$$coprod.map (id_W) (f ≫ g) = coprod.map f (id_W) ≫ coprod.map g (id_W).$$$

Lean4

@[reassoc]
theorem map_id_comp {X Y Z W : C} (f : X ⟶ Y) (g : Y ⟶ Z) [HasBinaryCoproduct W X] [HasBinaryCoproduct W Y]
    [HasBinaryCoproduct W Z] : coprod.map (𝟙 W) (f ≫ g) = coprod.map (𝟙 W) f ≫ coprod.map (𝟙 W) g := by simp

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