Geodesic
Symmetric monoidal completions and the exponential principle among labeled combinatorial structures
Theory and applications of categories, Tome 11 (2003), pp. 397-419.

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

We generalize Dress and Müller's main result in Decomposable functors and the exponential principle. We observe that their result can be seen as a characterization of free algebras for certain monad on the category of species. This perspective allows to formulate a general exponential principle in a symmetric monoidal category. We show that for any groupoid G, the category of presheaves on the symmetric monoidal completion !G of G satisfies the exponential principle. The main result in Dress and Müller reduces to the case G = 1. We discuss two notions of functor between categories satisfying the exponential principle and express some well known combinatorial identities as instances of the preservation properties of these functors. Finally, we give a characterization of G as a subcategory of presheaves on !G.
Classification : 05A99, 18D10, 18D35
Keywords: symmetric monoidal categories, combinatorics 
@article{TAC_2003_11_a17,
     author = {Matias Menni},
     title = {Symmetric monoidal completions
and the exponential principle among labeled combinatorial structures},
     journal = {Theory and applications of categories},
     pages = {397--419},
     publisher = {mathdoc},
     volume = {11},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2003_11_a17/}
}
TY  - JOUR
AU  - Matias Menni
TI  - Symmetric monoidal completions
and the exponential principle among labeled combinatorial structures
JO  - Theory and applications of categories
PY  - 2003
SP  - 397
EP  - 419
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2003_11_a17/
LA  - en
ID  - TAC_2003_11_a17
ER  - 
%0 Journal Article
%A Matias Menni
%T Symmetric monoidal completions
and the exponential principle among labeled combinatorial structures
%J Theory and applications of categories
%D 2003
%P 397-419
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2003_11_a17/
%G en
%F TAC_2003_11_a17
Matias Menni. Symmetric monoidal completions
and the exponential principle among labeled combinatorial structures. Theory and applications of categories, Tome 11 (2003), pp. 397-419. http://geodesic.mathdoc.fr/item/TAC_2003_11_a17/