Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion f] {U : Y.Opens} {V : X.Opens}
  (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) {Z : CommRingCat}
  (h : Y.presheaf.obj (Opposite.op ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj V)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.appLE f U V e)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.appIso f V).inv h) =
    CategoryTheory.CategoryStruct.comp (Y.presheaf.map (CategoryTheory.homOfLE ⋯).op) h

Defined in

Mathlib.AlgebraicGeometry.OpenImmersion

Cited by

1 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.IsOpenImmersion