Theorems · Definition · category theory

CategoryTheory.Functor.IsEventuallyConstantTo

{J : Type u_1} →
  {C : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} J] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} C] → CategoryTheory.Functor J C → J → Prop

A functor F : J ⥤ C is eventually constant to j : J if for any map f : i ⟶ j, the induced morphism F.map f is an isomorphism. If J is cofiltered, this implies F has a limit.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant

Cited by

19 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category