Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Modules.restrictFunctorComp

{X Y Z : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    (g : Y ⟶ Z) →
      [inst : AlgebraicGeometry.IsOpenImmersion f] →
        [inst_1 : AlgebraicGeometry.IsOpenImmersion g] →
          AlgebraicGeometry.Scheme.Modules.restrictFunctor (CategoryTheory.CategoryStruct.comp f g) ≅
            (AlgebraicGeometry.Scheme.Modules.restrictFunctor g).comp
              (AlgebraicGeometry.Scheme.Modules.restrictFunctor f)

Restriction along the composition is isomorphic to the composition of restrictions.

Defined in

Mathlib.AlgebraicGeometry.Modules.Sheaf

Cited by

4 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.IsOpenImmersionAlgebraicGeometry.IsOpenImmersion