Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.HasSheafCompose.isSheaf

∀ {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} [self : J.HasSheafCompose F] (P : CategoryTheory.Functor Cᵒᵖ A),
  CategoryTheory.Presheaf.IsSheaf J P → CategoryTheory.Presheaf.IsSheaf J (P.comp F)

For every sheaf P, P ⋙ F is a sheaf.

Defined in

Mathlib.CategoryTheory.Sites.Whiskering

Cited by

4 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.GrothendieckTopology.HasSheafCompose