equalizerCondition_profinite — Mathlib

English

If X is a sheaf on coherent topology over Profinite, then X.val satisfies the equalizer condition.

Русский

Если X является sheaf для когерентной топологии над Profinite, то X.val удовлетворяет равнительному условию.

LaTeX

$$$$\operatorname{EqualizerCondition}_{\mathrm{Profinite}}(X).$$$$

Lean4

/-- A condensed object regarded as a sheaf on `Profinite` satisfies the equalizer condition. -/
theorem equalizerCondition_profinite (X : Sheaf (coherentTopology Profinite.{u}) A) : EqualizerCondition X.val :=
  isSheaf_iff_preservesFiniteProducts_and_equalizerCondition X.val |>.mp X.cond |>.2

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