The Computation of the Möbius Function of a Möbius Category

On the Categorification of the Möbius Function

“…Since a monoid is just a category with one object, the theory of finite decomposition monoids embeds into the theory of Möbius categories. The notion of Möbius categories was introduced by Leroux in [10,24], and since then there have been quite a few publications in the field, among them [15,20,23,33]. Here we limit ourselves to the most basic results on Möbius categories.…”