Theorems · Definition · category theory

CategoryTheory.Functor.IsDenseSubsite.mapPreimage

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {J : CategoryTheory.GrothendieckTopology C} →
          (K : CategoryTheory.GrothendieckTopology D) →
            (G : CategoryTheory.Functor C D) →
              {A : Type u_4} →
                [inst_2 : CategoryTheory.Category.{v_4, u_4} A] →
                  [CategoryTheory.Functor.IsDenseSubsite J K G] →
                    (F : CategoryTheory.Sheaf J A) →
                      {X Y : C} → (G.obj X ⟶ G.obj Y) → (F.obj.obj (Opposite.op Y) ⟶ F.obj.obj (Opposite.op X))

If G : C ⥤ D is a dense subsite and F a sheaf on C, this is the morphism F.val.obj (op Y) ⟶ F.val.obj (op X) induced by a morphism G.obj X ⟶ G.obj Y in the category D.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

23 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite