instQuasiCompactLiftSchemeIdOfQuasiSeparatedSpaceCarrierCarrierCommRingCat

English

If X is a qcqs scheme, then the diagonal morphism Δ: X → X × X is quasi-compact.

Русский

Если X квазиразделима и компактна, то диагональ X → X × X квазиуплотна.

LaTeX

$$$[\\text{QuasiSeparatedSpace } X] \\Rightarrow \\mathrm{QuasiCompact}(\\mathrm{prod.lift}(\\mathrm{id}_X, \\mathrm{id}_X)).$$$

Lean4

instance [QuasiSeparatedSpace X] : QuasiCompact (prod.lift (𝟙 X) (𝟙 X)) := by
  rwa [← quasiSeparatedSpace_iff_quasiCompact_prod_lift]

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