preservesEpimorphisms_of_adjunction

English

If F ⊣ G is an adjunction, then F preserves epimorphisms.

Русский

Если F ⊣ G — глия, то F сохраняет эпиморфизмы.

LaTeX

$$PreservesEpimorphisms F$$

Lean4

theorem preservesEpimorphisms_of_adjunction {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G) : PreservesEpimorphisms F :=
  {
    preserves := fun {X} {Y} f hf =>
      ⟨by
        intro Z g h H
        replace H := congr_arg (adj.homEquiv X Z) H
        rwa [adj.homEquiv_naturality_left, adj.homEquiv_naturality_left, cancel_epi, Equiv.apply_eq_iff_eq] at H⟩ }

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