unital category

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 $(id_X,0) : X\to X\times Y$, $(0,id_Y): Y\to X\times Y$ is (jointly) strongly epimorphic.

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

- Francis Borceux, Dominique Bourn,
*Mal’cev, protomodular, homological and semi-abelian categories*, Mathematics and Its Applications**566**, Kluwer 2004

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)