Theorems · Theorem · algebraic geometry
AlgebraicGeometry.tilde.toOpen_map_app_assoc
∀ {R : CommRingCat} {M N : ModuleCat ↑R} (f : M ⟶ N) (U : TopologicalSpace.Opens (PrimeSpectrum ↑R)) {Z : ModuleCat ↑R}
(h : (AlgebraicGeometry.modulesSpecToSheaf.obj (AlgebraicGeometry.tilde N)).obj.obj (Opposite.op U) ⟶ Z),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen M U)
(CategoryTheory.CategoryStruct.comp
((AlgebraicGeometry.modulesSpecToSheaf.map (AlgebraicGeometry.tilde.map f)).hom.app (Opposite.op U)) h) =
CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen N U) h)- Defined in
- Mathlib.AlgebraicGeometry.Modules.Tilde
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- TopCat.carrierstatement · cited by 3,184
- CommRingCatstatement and proof · cited by 2,333
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
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