lift_fac — Mathlib

English

A nested lift through images satisfies the composition with another image-ι equals the image-ι of the composite: image.lift { I := image g, m := ι g, e := (f ≫ h) } ≫ image.ι g = image.ι (f ≫ g).

Русский

Сложное поднятие через образы удовлетворяет композиции: image.lift { ... } ≫ image.ι g = image.ι (f ≫ g).

LaTeX

$$$\mathrm{image.lift}\{ I := \mathrm{image} g, m := \iota g, e := (f \ggg h) \} \;\; \; \; \; \; \; \; \; \; \; \Rightarrow \; \; \; \; \; \; \; \; image.\mathrm{ι} (f \ggg g).$$$

Lean4

@[reassoc (attr := simp)]
theorem lift_fac (F' : MonoFactorisation f) : image.lift F' ≫ F'.m = image.ι f :=
  (Image.isImage f).lift_fac F'

Похожие утверждения