pullbackObjIsDefined_free_yoneda — Mathlib

English

A particular pullback object at a free Yoneda object is defined via pushforward with corepresentability.

Русский

Определён пуллбек на свободном Yoneda-объекте через pushforward иcorepresentability.

LaTeX

$$$\\mathrm{pullbackObjIsDefined}(\\varphi, (\\mathrm{free} S).\\mathrm{obj}(\\mathrm{yoneda}.X))$$$

Lean4

theorem pullbackObjIsDefined_free_yoneda (X : C) : pullbackObjIsDefined φ ((free S).obj (yoneda.obj X)) :=
  (pushforwardCompCoyonedaFreeYonedaCorepresentableBy φ X).isCorepresentable

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