Theorems · Definition · category theory

CategoryTheory.Functor.sheafPushforwardContinuous

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          (A : Type u) →
            [inst_2 : CategoryTheory.Category.{t, u} A] →
              (J : CategoryTheory.GrothendieckTopology C) →
                (K : CategoryTheory.GrothendieckTopology D) →
                  [F.IsContinuous J K] → CategoryTheory.Functor (CategoryTheory.Sheaf K A) (CategoryTheory.Sheaf J A)

The induced functor Sheaf K A ⥤ Sheaf J A given by F.op ⋙ _ if F is a continuous functor.

Defined in

Mathlib.CategoryTheory.Sites.Continuous

Cited by

102 results in Mathlib

Foundations

Depth 70 from the axioms, rests on 1,542 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsContinuous