instHasFunctorialFactorizationLocallySurjectiveLocallyInjective

English

Under suitable hypotheses, IsLocallySurjective φ is equivalent to Epi φ.

Русский

При подходящих гипотезах IsLocallySurjective φ равноэпиморфизмом эквивалентно Epi φ.

LaTeX

$$$$ IsLocallySurjective(\phi) \iff Epi(\phi) $$$$

Lean4

instance : (locallySurjective J A).HasFunctorialFactorization (locallyInjective J A) where
  nonempty_functorialFactorizationData :=
    ⟨functorialLocallySurjectiveInjectiveFactorization J (MorphismProperty.functorialFactorizationData _ _)⟩

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