Theorems · Theorem · algebraic geometry

AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE

∀ {R : CommRingCat} (f g x : ↑R) (hx : x = f * g),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.basicOpenIsoSpecAway x).inv
      ((AlgebraicGeometry.Spec R).homOfLE ⋯) =
    CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (IsLocalization.Away.awayToAwayRight f g)))
      (AlgebraicGeometry.basicOpenIsoSpecAway f).inv

Defined in: Mathlib.AlgebraicGeometry.Restrict
Cited by: 1 results in Mathlib
Foundations: Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites28

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
CommRingproof · cited by 17,173
RingHomproof · cited by 10,189
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
Algebra.algebraMapproof · cited by 4,706
AlgebraicGeometry.Schemestatement · cited by 2,540
CommRingCatstatement and proof · cited by 2,333
CommRingCat.carrierstatement and proof · cited by 1,096
RingHom.compproof · cited by 899
AlgebraicGeometry.Specstatement and proof · cited by 626

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assocproof · cited by 1