nLab
bi-initial object

Context

2-Category theory

Limits and colimits

Contents

Idea

Bi-initial objects are the bicategorical analogues of initial objects in categories.

Definition

In a bicategory AA, an object LAL \in A is bi-initial (or biinitial) when for all XAX \in A, there is an equivalence of categories between A(L,X)A(L,X) and the terminal category with a single object and single morphism 𝟙\mathbb{1}.

References

This concept appears among others in: