reflectsColimits_of_isEquivalence

English

There is an instance ensuring a pair is coreflexive for a right adjoint setting.

Русский

Существует инстанс, обеспечивающийcoreflexive пару в условиях правого сопряжения.

LaTeX

$$$$\\text{IsCoreflexivePair}(U'.map(F.map(\\eta_X)), otherMap(R,Adj))$$$$

Lean4

noncomputable instance (priority := 100) _root_.CategoryTheory.Functor.reflectsColimits_of_isEquivalence (E : D ⥤ C)
    [E.IsEquivalence] : ReflectsColimitsOfSize.{v, u} E where
  reflectsColimitsOfShape :=
    {
      reflectsColimit :=
        { reflects := fun t => ⟨(isColimitOfPreserves E.inv t).mapCoconeEquiv E.asEquivalence.unitIso.symm⟩ } }
      -- see Note [lower instance priority]

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