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,YX,Y the pair of maps (id X,0):XX×Y(id_X,0) : X\to X\times Y, (0,id Y):YX×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

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

Last revised on July 25, 2011 at 15:46:44. See the history of this page for a list of all contributions to it.