Theorems · Theorem · algebraic geometry
TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst
∀ {X : TopCat} (F : TopCat.Sheaf CommRingCat X) (U V : TopologicalSpace.Opens ↑X)
(x : ↑(F.obj.obj (Opposite.op (U ⊔ V)))),
(↑((CategoryTheory.ConcreteCategory.hom (F.objSupIsoProdEqLocus U V).hom) x)).1 =
(CategoryTheory.ConcreteCategory.hom (F.obj.map (CategoryTheory.homOfLE ⋯).op)) x- Defined in
- Mathlib.Topology.Sheaves.CommRingCat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- RingHomstatement · cited by 10,189
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement and proof · cited by 2,333
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- Quiver.Hom.opstatement and proof · cited by 1,948
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