nLab 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.

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