Theorems · Definition · category theory

CategoryTheory.SmallObject.functorObjLeftFamily

{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) →
              (x : CategoryTheory.SmallObject.FunctorObjIndex f πX) →
                CategoryTheory.SmallObject.functorObjSrcFamily f πX x ⟶
                  CategoryTheory.SmallObject.functorObjTgtFamily f πX x

The family of the morphisms f x.i : A x.i ⟶ B x.i parametrized by x : FunctorObjIndex f πX.

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

3 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.Category