Complete multiplicativity and complete additivity in Möbius categories. (English) Zbl 0955.05007

Schwab, Emil Daniel

Ital. J. Pure Appl. Math. 3, 37-48 (1998).

Summary: We prove characterizations of Lambek-Carlitz type for the completely multiplicative and the completely additive incidence functions in Möbius categories. In the case of a binomial-triangular category, we give a characterization of \(c\ell(x)\) as a completely additive incidence function (\(\ell(\alpha)\) is the length of the morphism \(\alpha\)). Finally we establish characterizations of Lambek-Carlitz type for \({\mathcal C}\)-binomial multiplicative and \({\mathcal C}\)-binomial additive formal power series via a full Möbius category of binomial type.

MSC:

18B99	Special categories
06A07	Combinatorics of partially ordered sets
11A25	Arithmetic functions; related numbers; inversion formulas

Keywords:

complete multiplicativity; complete additivity; incidence functions; Möbius categories; Lambek-Carlitz type