Geodesic
Finite sets and symmetric simplicial sets
Theory and applications of categories, Tome 8 (2001), pp. 244-252.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 18G30, 55U10, 18D10, 20F05.
Keywords: Simplicial sets, monoidal categories, generators and relations. 
@article{TAC_2001_8_a7,
     author = {Marco Grandis},
     title = {Finite sets and symmetric simplicial sets},
     journal = {Theory and applications of categories},
     pages = {244--252},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a7/}
}
TY  - JOUR
AU  - Marco Grandis
TI  - Finite sets and symmetric simplicial sets
JO  - Theory and applications of categories
PY  - 2001
SP  - 244
EP  - 252
VL  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2001_8_a7/
LA  - en
ID  - TAC_2001_8_a7
ER  - 
%0 Journal Article
%A Marco Grandis
%T Finite sets and symmetric simplicial sets
%J Theory and applications of categories
%D 2001
%P 244-252
%V 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2001_8_a7/
%G en
%F TAC_2001_8_a7
Marco Grandis. Finite sets and symmetric simplicial sets. Theory and applications of categories, Tome 8 (2001), pp. 244-252. http://geodesic.mathdoc.fr/item/TAC_2001_8_a7/