equalizerSubobject_arrow_comp — Mathlib

English

Let f,g: X → Y with HasEqualizer f g. The equalizerSubobject arrow equalizes f and g: (equalizerSubobject f g).arrow ≫ f = (equalizerSubobject f g).arrow ≫ g.

Русский

Пусть f,g: X → Y с HasEqualizer f g. Стрела подобъекта эквалайзера равенства делает равенство: (equalizerSubobject f g).arrow ≫ f = (equalizerSubobject f g).arrow ≫ g.

LaTeX

$$$$(equalizerSubobject f g).arrow \\;\\text{is an equalizer: } (equalizerSubobject f g).arrow \\;\\circ f = (equalizerSubobject f g).arrow \\;\\circ g$$$$

Lean4

@[reassoc]
theorem equalizerSubobject_arrow_comp : (equalizerSubobject f g).arrow ≫ f = (equalizerSubobject f g).arrow ≫ g := by
  rw [← equalizerSubobject_arrow, Category.assoc, Category.assoc, equalizer.condition]

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