Theorems · Theorem · algebraic geometry

AlgebraicGeometry.SheafedSpace.IsOpenImmersion.inv_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 ↑↑X.toPresheafedSpace),
  CategoryTheory.inv (AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp f U) =
    CategoryTheory.CategoryStruct.comp
      (f.hom.c.app (Opposite.op ((AlgebraicGeometry.SheafedSpace.IsOpenImmersion.opensFunctor f).obj U)))
      (X.presheaf.map (CategoryTheory.eqToHom ⋯))

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.SheafedSpace.IsOpenImmersion