Theorems · Definition · category theory

CategoryTheory.Sheaf.composeAndSheafify

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      {A : Type u_1} →
        {B : Type u_2} →
          [inst_1 : CategoryTheory.Category.{v_1, u_1} A] →
            [inst_2 : CategoryTheory.Category.{v_2, u_2} B] →
              CategoryTheory.Functor A B →
                [CategoryTheory.HasWeakSheafify J B] →
                  CategoryTheory.Functor (CategoryTheory.Sheaf J A) (CategoryTheory.Sheaf J B)

This is the functor sending a sheaf X : Sheaf J A to the sheafification of X.val ⋙ F.

Defined in

Mathlib.CategoryTheory.Sites.PreservesSheafification

Cited by

7 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify