Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le

∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U) (V : X.Opens) (h : U ≤ V),
  AlgebraicGeometry.Scheme.Hom.app hU.fromSpec V =
    CategoryTheory.CategoryStruct.comp (X.presheaf.map (CategoryTheory.homOfLE h).op)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.ΓSpecIso (X.presheaf.obj (Opposite.op U))).inv
        ((AlgebraicGeometry.Spec (X.presheaf.obj (Opposite.op U))).presheaf.map (CategoryTheory.homOfLE ⋯).op))

Defined in

Mathlib.AlgebraicGeometry.AffineScheme

Cited by

2 results in Mathlib

Foundations

Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound