isSheafUniqueGluing — Mathlib

English

A streamlined equivalence between IsSheaf and IsSheafUniqueGluing with simp lemmas.

Русский

Упрощенная эквивалентность IsSheaf и IsSheafUniqueGluing с помощью simp-лемм.

LaTeX

$$$$\text{IsSheaf } F \iff \text{IsSheafUniqueGluing } F,$$$$

Lean4

theorem isSheafUniqueGluing (h : F.IsSheaf) {ι : Type*} (U : ι → Opens X) (sf : ∀ i : ι, ToType (F.obj (op (U i))))
    (cpt : IsCompatible F U sf) : ∃! s : ToType (F.obj (op (iSup U))), IsGluing F U sf s :=
  ((isSheaf_iff_isSheaf_comp' (forget C) F).mp h).isSheafUniqueGluing_types sf cpt

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