Theorems · Theorem · algebraic geometry
AlgebraicGeometry.essImage_bialgSpec
∀ {R : CommRingCat} {G : CategoryTheory.Mon (CategoryTheory.Over (AlgebraicGeometry.Spec R))},
(AlgebraicGeometry.bialgSpec R).essImage G ↔ AlgebraicGeometry.IsAffine G.X.leftThe essential image of R-bialgebras under Spec is precisely affine monoid schemes over
Spec R.
- Defined in
- Mathlib.AlgebraicGeometry.Group.Affine
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oppositestatement · cited by 8,081
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.Overstatement and proof · cited by 935
- AlgebraicGeometry.Specstatement and proof · cited by 626
- CategoryTheory.Over.leftstatement and proof · cited by 541
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.Xstatement and proof · cited by 329
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- CategoryTheory.Functor.essImagestatement · cited by 82
- CommBialgCatstatement · cited by 38
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.