Theorems · Definition · category theory

CategoryTheory.sheafCompose

{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 : CategoryTheory.Functor A B) →
                [J.HasSheafCompose F] → CategoryTheory.Functor (CategoryTheory.Sheaf J A) (CategoryTheory.Sheaf J B)

Composing a functor which HasSheafCompose, yields a functor between sheaf categories.

Defined in

Mathlib.CategoryTheory.Sites.Whiskering

Cited by

28 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.GrothendieckTopology.HasSheafCompose