eq_of_epi_equalizer — Mathlib

English

If HasEqualizer f g and equalizer.ι f g is epi, then f = g.

Русский

Если существует равножка равеных f,g и равножка ι f g эпиморфна, то f = g.

LaTeX

$$[HasEqualizer f g] ∧ Epi (equalizer.ι f g) ⇒ f = g$$

Lean4

/-- If the equalizer of two morphisms is an epimorphism, then the two morphisms are equal. -/
theorem eq_of_epi_equalizer [HasEqualizer f g] [Epi (equalizer.ι f g)] : f = g :=
  (cancel_epi (equalizer.ι f g)).1 <| equalizer.condition _ _

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