The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal symmetric monoid, or by generators and relations. The latter provides a definition of symmetric simplicial sets by faces, degeneracies and transpositions, under suitable relations.
Theory and Applications of Categories, Vol. 8, 2001, No. 8, pp 244-252 http://www.tac.mta.ca/tac/volumes/8/n8/n8.dvi http://www.tac.mta.ca/tac/volumes/8/n8/n8.ps http://www.tac.mta.ca/tac/volumes/8/n8/n8.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n8/n8.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n8/n8.psTAC Home