Theorems · Definition · category theory

CategoryTheory.SmallObject.functorMap

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {I : Type w} →
      {A B : I → C} →
        (f : (i : I) → A i ⟶ B i) →
          {S T X Y : C} →
            {πX : X ⟶ S} →
              {πY : Y ⟶ T} →
                (CategoryTheory.Arrow.mk πX ⟶ CategoryTheory.Arrow.mk πY) →
                  [inst_1 :
                      CategoryTheory.Limits.HasColimitsOfShape
                        (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX)) C] →
                    [inst_2 :
                        CategoryTheory.Limits.HasColimitsOfShape
                          (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πY)) C] →
                      [inst_3 :
                          CategoryTheory.Limits.HasPushout (CategoryTheory.SmallObject.functorObjTop f πX)
                            (CategoryTheory.SmallObject.functorObjLeft f πX)] →
                        [inst_4 :
                            CategoryTheory.Limits.HasPushout (CategoryTheory.SmallObject.functorObjTop f πY)
                              (CategoryTheory.SmallObject.functorObjLeft f πY)] →
                          CategoryTheory.SmallObject.functorObj f πX ⟶ CategoryTheory.SmallObject.functorObj f πY

The functor SmallObject.functor f S : Arrow S ⥤ Arrow S that is part of the small object argument for a family of morphisms f, on morphisms.

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasPushoutCategoryTheory.Limits.HasPushout