Theorems · Definition · category theory

CategoryTheory.SmallObject.functor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {I : Type w} →
      {A B : I → C} →
        (f : (i : I) → A i ⟶ B i) →
          [CategoryTheory.Limits.HasPushouts C] →
            [∀ {X S : C} (πX : X ⟶ S),
                  CategoryTheory.Limits.HasColimitsOfShape
                    (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX)) C] →
              CategoryTheory.Functor (CategoryTheory.Arrow C) (CategoryTheory.Arrow C)

The functor Arrow C ⥤ Arrow C that is constructed in order to apply the small object argument to a family of morphisms f i : A i ⟶ B i, see the introduction of the file Mathlib/CategoryTheory/SmallObject/Construction.lean

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

6 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasColimitsOfShape