Theorems · Definition · category theory

CategoryTheory.SmallObject.functorObjTgtFamily

{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) → CategoryTheory.SmallObject.FunctorObjIndex f πX → C

The family of objects B x.i parametrized by x : FunctorObjIndex f πX.

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

30 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Category