Lawvere intervals and the Möbius function of a Möbius category
Lawvere intervals of a Möbius category are finite one-way categories. We investigate a simple connection between the Möbius function of a Möbius category and the Möbius functions of its Lawvere intervals. In this investigation we have taken into consideration that a large class of Möbius categories arise as skeletons of division categories (that are right cancellative with pushouts). In general, the computation of the Möbius function for a Möbius category is laborious. In our case it becomes a routine computation on finite lattices. As an illustration, the results of this study may be used to compute the Möbius function of a proper Möbius category.