Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ext_of_apply_closedPoint_eq

∀ {X : AlgebraicGeometry.Scheme} {K : Type u} [inst : Field K] [IsAlgClosed K]
  {f g : AlgebraicGeometry.Spec (CommRingCat.of K) ⟶ X} (h : X ⟶ AlgebraicGeometry.Spec (CommRingCat.of K))
  [AlgebraicGeometry.LocallyOfFiniteType h],
  CategoryTheory.CategoryStruct.comp f h =
      CategoryTheory.CategoryStruct.id (AlgebraicGeometry.Spec (CommRingCat.of K)) →
    CategoryTheory.CategoryStruct.comp g h =
        CategoryTheory.CategoryStruct.id (AlgebraicGeometry.Spec (CommRingCat.of K)) →
      f (IsLocalRing.closedPoint K) = g (IsLocalRing.closedPoint K) → f = g

Defined in

Mathlib.AlgebraicGeometry.AlgClosed.Basic

Cited by

2 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsAlgClosedAlgebraicGeometry.LocallyOfFiniteType