Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, 79968-0514, USA
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in M\"o\-bius categories of full binomial type. The $q$-analog of the Lambek-Carlitz type characterization of exponential series is also established.
AMSclassification. 11A25, 18B99, 13F25.
Keywords. Completely multiplicative functions, M\"o\-bius categories, exponential series.