nLab bi-terminal object

Idea

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

Definition

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

Related concepts

• terminal object

• bi-initial object

• terminal 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).