Theorems · Theorem · algebraic geometry
AlgebraicGeometry.diagonal_SpecMap
∀ (R S : Type u) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
CategoryTheory.Limits.pullback.diagonal (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (algebraMap R S))) =
CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Spec.map (CommRingCat.ofHom (Algebra.TensorProduct.lmul' R).toRingHom))
(AlgebraicGeometry.pullbackSpecIso R S S).inv- Defined in
- Mathlib.AlgebraicGeometry.Pullbacks
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites35
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.CategoryStruct.compstatement and proof · cited by 17,999
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- TensorProductstatement · cited by 2,545
- AlgebraicGeometry.Schemestatement · cited by 2,540
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