Theorems · Theorem · algebraic geometry
AlgebraicGeometry.morphismRestrict_app
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (U : Y.Opens) (V : (↑U).Opens),
AlgebraicGeometry.Scheme.Hom.app (f ∣_ U) V =
CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Scheme.Hom.app f ((AlgebraicGeometry.Scheme.Hom.opensFunctor U.ι).obj V))
(X.presheaf.map (CategoryTheory.eqToHom ⋯).op)- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.morphismRestrict_app'proof · cited by 5
- AlgebraicGeometry.targetAffineLocally_affineAnd_iffproof · cited by 4
- AlgebraicGeometry.morphismRestrict_appTopproof · cited by 3
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2