Theorems · Definition · category theory

SheafOfModules.overFunctorMap

{D : Type u₂} →
  [inst : CategoryTheory.Category.{v₂, u₂} D] →
    {K : CategoryTheory.GrothendieckTopology D} →
      (R : CategoryTheory.Sheaf K RingCat) →
        {X Y : D} →
          (f : X ⟶ Y) →
            (SheafOfModules.overFunctor R Y).comp (SheafOfModules.overMap R f) ≅ SheafOfModules.overFunctor R X

First restricting to Over Y and then extending to Over X is the same as restricting to Over X.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category