Theorems · Definition · category theory

CategoryTheory.Functor.isInitial

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {F : CategoryTheory.Functor C D} →
          ((X : C) → CategoryTheory.Limits.IsInitial (F.obj X)) → CategoryTheory.Limits.IsInitial F

If F : C ⥤ D is such that F.obj X is initial for any X : C, then F is an initial object.

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Terminal

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category