instPreservesColimitsOfSizeUliftFunctor

English

The functor uliftFunctor preserves colimits of arbitrary size.

Русский

Функтор uliftFunctor сохраняет конилоиды произвольного размера.

LaTeX

$$$\mathrm{PreservesColimitsOfSize}(\mathrm{uliftFunctor})$$$

Lean4

/-- The functor `uliftFunctor : Type u ⥤ Type (max u v)` preserves colimits of arbitrary size.
-/
noncomputable instance : PreservesColimitsOfSize.{w', w} uliftFunctor.{v, u} where
  preservesColimitsOfShape
    {J
      _} :=
    {
      preservesColimit := fun {F} ↦
        {
          preserves := fun {c} hc ↦ by
            rw [isColimit_iff_coconeTypesIsColimit]
            exact
              (((isColimit_iff_coconeTypesIsColimit _).1 ⟨hc⟩).precompose (G := F ⋙ uliftFunctor.{v})
                    (fun _ ↦ Equiv.ulift) (fun _ ↦ rfl)).of_equiv
                Equiv.ulift.symm (fun _ _ ↦ rfl) } }

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