Moebius inversion in general categories
Dr A. Tonks (London Metropolitan University)
Monday 11th March, 2013 16:00-17:00 Mathematics 203
Moebius inversion is a method for inverting numerical functions defined over a poset $P$, generalising the inclusion-exclusion principle (if $P$ is a power set) and the classical number-theoretical Moebius function (if $P$ is the positive integers, ordered by divisibility). Leroux considered a notion of Moebius category $P$ for which an analogous theory exists, but required certain finiteness conditions that exclude important examples such as the category of trees. In this talk we give a theory which avoids these finiteness conditions, by working with groupoid coefficients instead of numbers, and using techniques with a homotopy rather than a combinatorial flavour.