eq_valuativeCriterion — Mathlib

English

The UniversallyClosed criterion can be decomposed as UniversallyClosed = ValuativeCriterion ∧ QuasiCompact, expressing the interplay of valuative and compactness conditions.

Русский

Критерий универсальности может разлагаться как UniversallyClosed = ValuativeCriterion ∧ QuasiCompact, выражая взаимное влияние валюативности и компактности.

LaTeX

$$$\mathrm{UniversallyClosed} = \mathrm{ValuativeCriterion} \wedge \mathrm{QuasiCompact}$$$

Lean4

/-- The **valuative criterion** for universally closed morphisms. -/
@[stacks 01KF]
theorem eq_valuativeCriterion : @UniversallyClosed = ValuativeCriterion.Existence ⊓ @QuasiCompact := by
  rw [universallyClosed_eq_universallySpecializing, ValuativeCriterion.Existence.eq]

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