Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Spec.map_inv
∀ {R S : CommRingCat} (f : R ⟶ S) [inst : CategoryTheory.IsIso f],
AlgebraicGeometry.Spec.map (CategoryTheory.inv f) = CategoryTheory.inv (AlgebraicGeometry.Spec.map f)- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.IsIso
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.objproof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.Specstatement · cited by 626
- CategoryTheory.invstatement and proof · cited by 467
- AlgebraicGeometry.Spec.mapstatement · cited by 332
- AlgebraicGeometry.Scheme.Specproof · cited by 57
- CategoryTheory.Functor.map_invproof · cited by 38
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.SpecMap_ΓSpecIso_homproof · cited by 8
- AlgebraicGeometry.Scheme.PartialMap.equiv_of_fromSpecStalkOfMem_eqproof · cited by 1
- AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_ιproof · cited by 1