uliftYonedaFunctor_preservesLimits

English

The composition of the Yoneda embedding with the ultrift construction preserves limits; i.e., uliftYoneda has preservesLimits when composed with Yoneda.

Русский

Образование ультифута через Yoneda сохраняет пределы: композиция uliftYoneda и Yoneda сохраняет пределы.

LaTeX

$$$\\mathrm{PreservesLimits}(\\mathrm{uliftYoneda})$$$

Lean4

instance uliftYonedaFunctor_preservesLimits : PreservesLimitsOfSize.{t, w} (uliftYoneda.{w'} : C ⥤ _) :=
  by
  apply preservesLimits_of_evaluation
  intro K
  change PreservesLimitsOfSize.{t, w} (coyoneda.obj K ⋙ uliftFunctor.{w'})
  infer_instance

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