Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.inv_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] {U V : (TopologicalSpace.Opens ↑↑X)ᵒᵖ} (i : U ⟶ V) {Z : C}
  (h :
    Y.presheaf.obj
        (Opposite.op ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).obj (Opposite.unop V))) ⟶
      Z),
  CategoryTheory.CategoryStruct.comp (X.presheaf.map i)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp f (Opposite.unop V))
        h) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp f (Opposite.unop U))
      (CategoryTheory.CategoryStruct.comp
        (Y.presheaf.map ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).op.map i)) h)

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion