Theorems · Theorem · category theory
TopCat.Presheaf.isSheaf_of_isSheafUniqueGluing_types
∀ {X : TopCat} (F : TopCat.Presheaf (Type u_4) X), F.IsSheafUniqueGluing → F.IsSheafThe usual sheaf condition can be obtained from the sheaf condition in terms of unique gluings.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCatstatement and proof · cited by 1,889
- TypeCat.Funstatement · cited by 1,307
- TopCat.Presheafstatement and proof · cited by 371
- TopCat.Presheaf.IsSheafstatement · cited by 38
- TopCat.Presheaf.IsSheafUniqueGluingstatement and proof · cited by 3
- TopCat.Presheaf.isSheaf_iff_isSheafUniqueGluing_typesproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.toTypes_isSheafproof · cited by 1
- TopCat.subpresheafToTypes.isSheafproof · cited by 0