Symmetric monoidal completions and the exponential principle among labeled combinatorial structures

Título:

Symmetric monoidal completions and the exponential principle among labeled combinatorial structures

Autor:

Menni, Matías

Colaboradores:

; 

Temas:

TEORÍA DE CATEGORÍASMATEMÁTICA DE LA COMPUTACIÓN

En:

Theory and Applications of Categories, Vol. 11, No. 18, 2003, pp. 397–419.

Resumen:

We generalize Dress and M¨uller’s main result in [5]. 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 !G of presheaves on the symmetric monoidal completion !G of G satisfies the exponential principle. The main result in [5] 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 !G.

URL/DOI:

Medio:

Soporte electrónico

Tipo de documento:

Artículo

Idioma:

Inglés

Publicación:

, 2003

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