# nLab bi-initial object

Contents

### Context

#### 2-Category theory

2-category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

#### Limits and colimits

limits and colimits

# Contents

## 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 $\mathbb{1}$.

## References

This concept appears among others in:

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

Last revised on October 3, 2021 at 09:14:19. See the history of this page for a list of all contributions to it.