Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] (U : TopologicalSpace.Opens ↑↑X) {Z : C}
  (h :
    ((TopCat.Presheaf.pushforward C f.base).obj X.presheaf).obj
        (Opposite.op ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).obj U)) ⟶
      Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp f U)
      (CategoryTheory.CategoryStruct.comp
        (f.c.app (Opposite.op ((AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor f).obj U))) h) =
    CategoryTheory.CategoryStruct.comp (X.presheaf.map (CategoryTheory.eqToHom ⋯)) h

Defined in

Mathlib.Geometry.RingedSpace.OpenImmersion

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion