Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict_hom_c_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] (X_1 : (TopologicalSpace.Opens ↑↑(Y.restrict ⋯))ᵒᵖ),
  (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isoRestrict f).hom.c.app X_1 =
    CategoryTheory.CategoryStruct.comp
      (f.c.app
        (Opposite.op ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).obj (Opposite.unop X_1))))
      (X.presheaf.map (CategoryTheory.eqToHom ⋯))

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion