nLab bi-initial object

Idea

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

Definition

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

Related concepts

• initial object

• bi-terminal object

• initial object in an $(\infty,1)$-category

References

This concept appears among others in:

• Tslil Clingman, Lyne Moser, 2-limits and 2-terminal objects are too different (arXiv:2004.01313)