Theorems · Definition · category theory

CategoryTheory.sheafCompose_map

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {A : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} A] →
        {B : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} B] →
            (J : CategoryTheory.GrothendieckTopology C) →
              {F G : CategoryTheory.Functor A B} →
                (F ⟶ G) →
                  [inst_3 : J.HasSheafCompose F] →
                    [inst_4 : J.HasSheafCompose G] → CategoryTheory.sheafCompose J F ⟶ CategoryTheory.sheafCompose J G

If η : F ⟶ G is a natural transformation then we obtain a morphism of functors sheafCompose J F ⟶ sheafCompose J G by whiskering with η on the level of presheaves.

Defined in

Mathlib.CategoryTheory.Sites.Whiskering

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.GrothendieckTopology.HasSheafComposeCategoryTheory.GrothendieckTopology.HasSheafCompose