Theorems · Definition · category theory

CategoryTheory.SmallObject.functorObj

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {I : Type w} →
      {A B : I → C} →
        (f : (i : I) → A i ⟶ B i) →
          {S X : C} →
            (πX : X ⟶ S) →
              [inst_1 :
                  CategoryTheory.Limits.HasColimitsOfShape
                    (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX)) C] →
                [CategoryTheory.Limits.HasPushout (CategoryTheory.SmallObject.functorObjTop f πX)
                      (CategoryTheory.SmallObject.functorObjLeft f πX)] →
                  C

The functor SmallObject.functor f : Arrow C ⥤ Arrow C that is part of the small object argument for a family of morphisms f, on an object given as a morphism πX : X ⟶ S.

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

30 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasPushout