localizedFunctor_isEquivalence — Mathlib

English

Under the Localization Lifting setup, F.Linear R and G.Linear R are equivalent properties depending on a chosen lift.

Русский

В условиях подъема локализации для F и G линейность по R эквивалентна в зависимости от подъема.

LaTeX

$$$F.Linear\ R \iff G.Linear\ R$$$

Lean4

/-- If a `LocalizerMorphism` is a localized equivalence, then the induced functor on
the localized categories is an equivalence -/
instance localizedFunctor_isEquivalence [Φ.IsLocalizedEquivalence] : (Φ.localizedFunctor L₁ L₂).IsEquivalence :=
  Φ.isEquivalence L₁ L₂ _

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