sheafCondition_of_sheaf — Mathlib

English

If F is a Sheaf J A, then S.SheafCondition F.val holds.

Русский

Если F — онакающий Sheaf J A, тогда S.SheafCondition F.val истинно.

LaTeX

$$S.SheafCondition F.val$$

Lean4

theorem sheafCondition_of_sheaf {A : Type u'} [Category.{v} A] (F : Sheaf J A) : S.SheafCondition F.val :=
  by
  rw [sheafCondition_iff_comp_coyoneda]
  intro X
  exact
    (Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff _ S.toSquare).1
      (S.isPushout.op.map (yoneda.obj ⟨_, (isSheaf_iff_isSheaf_of_type _ _).2 (F.cond X.unop)⟩))

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