category theory

# Contents

## Definition

A category is unital in the sense of Bourn if it has a zero object (is a pointed category), admits finite limits and for all objects $X,Y$ the pair of maps $\left({\mathrm{id}}_{X},0\right):X\to X×Y$, $\left(0,{\mathrm{id}}_{Y}\right):Y\to X×Y$ is (jointly) strongly epimorphic.

## References

This terminology is introduced in

• Dominique Bourn, Mal’cev categories and fibrations of pointed objects, Appl. Cate- gorical Structures 4 (1996) 302-327

Exposition is in the section 1.2 in

Unfortunately the terminology is not compatible with the notions of unitality of A-infinity categories.

Revised on July 25, 2011 15:46:44 by Urs Schreiber (89.204.153.119)