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Categorical aspects of generating functions(II) Operations on categories and functors
| Title: | Categorical aspects of generating functions(II) Operations on categories and functors |
| Authors: | Yoshida, T. Browse this author |
| Issue Date: | 1-Oct-1998 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 432 |
| Start Page: | 1 |
| End Page: | 65 |
| Abstract: | This paper is a sequel to the author's paper [Yos 98]. We construct some operations on categories and functors, for example, summation, multiplication, derivation, partial derivation, exponentiation, substitution. These operations are correspond to those of species. The main results of this paper are two theorems (Theorem 5.8, 6.5) which characterizing strict Krull-Schmidt categories(KS-categories). Especially, Theorem 6.5 states that for a skeletally small and locally finite category £ with finite coproducts and its full subcategory C, if the exponential formula E(t) = exp(C(t)) implies, under a technical assumption, that £ is a strict Krull-Schmidt category. Furthermore, we define the substitution T(S) of functors S : £---+ S and T : F--+ Seti, where S has finite coproducts. These operations satisfy formulas similar to such operations on the usual power series. There are some applications. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69182 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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