instIsClosedUnderQuotientsInverseImageOfPreservesEpimorphisms

English

If F: D ⥤ C preserves epimorphisms and P is closed under quotients, then the inverse image (P.inverseImage F) is closed under quotients.

Русский

Если F: D ⥤ C сохраняет эпиморфизмы, и P замкнуто по кваз-морфизмам, то P^{-1}F замкнуто по quotients.

LaTeX

$$$\forall F:D\to C\ [F.\PreservesEpimorphisms], (P.\inverseImage F).\IsClosedUnderQuotients.$$$

Lean4

instance (F : D ⥤ C) [F.PreservesEpimorphisms] : (P.inverseImage F).IsClosedUnderQuotients where
  prop_of_epi f _ h := P.prop_of_epi (F.map f) h

Похожие утверждения