instFullSheafFunctorOppositeCompSheafComposeSheafToPresheafOfFaithful

English

If F is faithful and full, then the composed functor (sheafCompose J F) followed by the forgetful functor is full.

Русский

Если F верен и полно, тогда композиция (sheafCompose J F) с забыванием полно.

LaTeX

$$$\mathrm{Full}\big( \mathrm{sheafToPresheaf} \circ \mathrm{sheafCompose}\, J\, F \big)$$$

Lean4

instance [F.Faithful] [F.Full] : (sheafCompose J F ⋙ sheafToPresheaf _ _).Full :=
  show (sheafToPresheaf _ _ ⋙ (whiskeringRight Cᵒᵖ A B).obj F).Full from inferInstance

Похожие утверждения