Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.comap

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {K : CategoryTheory.GrothendieckTopology D} →
          (Φ : K.Point) →
            (F : CategoryTheory.Functor C D) →
              [CategoryTheory.RepresentablyFlat F] →
                {J : CategoryTheory.GrothendieckTopology C} →
                  CategoryTheory.CoverPreserving J K F →
                    [CategoryTheory.InitiallySmall (F.comp Φ.fiber).Elements] → J.Point

If F : C ⥤ D is a representably flat and cover preserving functor between sites, then any point on D induces a point on C by precomposing the fiber functor with F.

Defined in

Mathlib.CategoryTheory.Sites.Point.Comap

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.RepresentablyFlatCategoryTheory.InitiallySmall