Categories of orbit types for proper Lie groupoids
  It is widely understood that the quotient space of a topological group action can have a complicated combinatorial structure, indexed somehow by the sotropy groups of the action, but how best to record this structure seems unclear. This sketch defines a database category of orbit types for a proper Lie groupoid (based on recent work with roots in the theory of geometric quantization) as an attempt to capture some of this information. 
Jack Morava
math.AT