Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.isAffine_of_isLimit
∀ {I : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} I] {D : CategoryTheory.Functor I AlgebraicGeometry.Scheme}
(c : CategoryTheory.Limits.Cone D) (hc : CategoryTheory.Limits.IsLimit c)
[∀ (i : I), AlgebraicGeometry.IsAffine (D.obj i)], AlgebraicGeometry.IsAffine c.pt- Defined in
- Mathlib.AlgebraicGeometry.Limits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Top.topproof · cited by 9,680
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Isoproof · cited by 3,963
- Equiv.symmproof · cited by 3,681
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isAffineHom_π_appproof · cited by 3
- AlgebraicGeometry.isBasis_preimage_isAffineOpenproof · cited by 1