English
The underlying topological points of the pullback correspond bijectively to pairs consisting of a point in X, a point in Y, and a prime spectrum data of their tensor product over the base.
Русский
Точки проективной вытяжки соответствуют биекции пар: точка в X, точка в Y и данные спектра притензий их тензора над базой.
LaTeX
$$$\uparrow(\mathrm{pullback}\ f\ g) \simeq \Sigma T:\mathrm{Triplet} f g, \mathrm{Spec} T.tensor$$$
Lean4
@[reassoc (attr := simp)]
theorem tensorCongr_SpecTensorTo {T T' : Triplet f g} (h : T = T') :
Spec.map (Triplet.tensorCongr h).hom ≫ T.SpecTensorTo = T'.SpecTensorTo :=
by
subst h
simp only [Triplet.tensorCongr_refl, Iso.refl_hom, Spec.map_id, Category.id_comp]