  We determine the structure of the Chan-Paton factors of the open strings
ending on space filling D-branes in Type II orientifolds. Through the analysis,
we obtain a rule concerning possible distribution of O-plane types. The result
is applied to classify the topology of D-branes in terms of Fredholm operators
and K-theory, deriving a proposal made earlier and extending it to more general
cases. It is also applied to compactifications with N=1 supersymmetry in
four-dimensions. We adapt and develop the language of category in this context,
and use it to describe some decay channels.
