essImage_eq_of_natIso — Mathlib

English

Same extensionality principle for essImage morphisms as in the previous entry.

Русский

Та же принцип экстерности для морфизмов essImage, как и в предыдущем пункте.

LaTeX

$$F.essImage.ι.map f = F.essImage.ι.map g ⇒ f = g$$

Lean4

/-- Isomorphic functors have equal essential images. -/
theorem essImage_eq_of_natIso {F' : C ⥤ D} (h : F ≅ F') : essImage F = essImage F' :=
  funext fun _ => propext ⟨essImage.ofNatIso h, essImage.ofNatIso h.symm⟩

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