open access

https://doi.org/10.14943/83578

https://hdl.handle.net/2115/69182

Categorical aspects of generating functions(II) Operations on categories and functors

英語

1998-10-01

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

432

1-65

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.

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