Hello, I've sent the following message to sci.math, but haven't received a clear answer. I've also tried sci.math.research, but the moderator bounced the posting. Possibly someone here can help? Derek. =============================================== I'm working through the following paper, trying to learn a bit more about category theory: Matrices, Monads and the Fast Fourier Transform http://citeseer.nj.nec.com/jay93matrice.html I this paper, the author explains vectors in categorical notation: "Vectors are distinguished from lists because their length is given as part of their structure, represented by a morphism (function) #: VA -> N." What this means is that the morphism '#' will produce the length of vector. However, does this violate one of the requirements that a morphism must preserve the structure of an object? A vector is a sequence of elements, and an integer is only a single value. Does this mean that an integer has the same structure as a vector? Or does "structure preserving morphism" mean something different? Thanks, Derek.