English
If Y is quasi-separated, then the equalizer morphism ι: Equalizer(f,g) → X has a quasi-compact carrier for any f,g: X → Y.
Русский
Если Y квазиразделима, то равнозначный морфизм ι: Equalizer(f,g) → X имеет квазиуплотную топологическуюCarrier.
LaTeX
$$$[\\mathrm{QuasiSeparatedSpace}(Y)] \\Rightarrow \\mathrm{QuasiCompact}(\\mathrm{equalizer.ι} \\, f \\, g).$$$
Lean4
instance [QuasiSeparatedSpace Y] (f g : X ⟶ Y) : QuasiCompact (equalizer.ι f g) :=
MorphismProperty.of_isPullback (P := @QuasiCompact) (isPullback_equalizer_prod f g).flip inferInstance
