Theorems · Theorem · algebraic geometry

AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.SheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.SheafedSpace.IsOpenImmersion f] (U : TopologicalSpace.Opens ↑↑Y.toPresheafedSpace),
  CategoryTheory.CategoryStruct.comp (f.hom.c.app (Opposite.op U))
      (AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp f ((TopologicalSpace.Opens.map f.hom.base).obj U)) =
    Y.presheaf.map (CategoryTheory.homOfLE ⋯).op

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.SheafedSpace.IsOpenImmersion