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Categorical aspects of generating functions (I) Exponential formulas and Krull-Schmidt categories

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83562

Title: Categorical aspects of generating functions (I) Exponential formulas and Krull-Schmidt categories
Authors: Yoshida, T. Browse this author
Issue Date: 1-Jun-1998
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 416
Start Page: 1
End Page: 44
Abstract: In this paper, we study formal power series with exponents in a category. For example, the generating function of a category E with finite Hom-sets is defined by E(t) = :Etx /IAut(X)I, where the summation is taken over all isomorphism classes of obejects of E. We can use such power series to enumerate the number of £-structures along a faithful functors(Theorem 4.6). Our theory is closely related to the thory of species (Joyal 1981). A species can be identified with a faithful functor from a groupoid to the category of finite sets (The­orem 3.6). We use mainly the concept of faithful functors with finite fibers instead of that of species, by which we can separate the roles which categories play and which functors play. For example, the ex­ponential formula E(t) = exp(Con(E)(t)) means the unique coproduct decomposition property(Theorem 5.8). In the final section, we give some applications of our theory to rather classical enumerations.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69166
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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