Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.fiber

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.LocallySmall.{w, v, u} C] →
      {N : Type u'} →
        [inst_2 : CategoryTheory.Category.{v', u'} N] →
          CategoryTheory.Functor N C → [CategoryTheory.InitiallySmall N] → CategoryTheory.Functor C (Type w)

Given a functor p : N ⥤ C, this is the functor C ⥤ Type w which sends X : C to the colimit of types of morphisms p.obj U ⟶ X for U : N.

Defined in

Mathlib.CategoryTheory.Sites.Point.OfIsCofiltered

Cited by

9 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.CategoryCategoryTheory.InitiallySmall