The function # should not have been referred to as a morphism. It is an operation. Operations must be preserved by morphisms, but operations need not be morphisms themselves. (In fact a distributive law is a statement that some operation is a morphism with respect to another operation.) -Charles Wells
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.
Charles Wells, Emeritus Professor of Mathematics, Case Western Reserve University Affiliate Scholar, Oberlin College Send all mail to: 105 South Cedar St., Oberlin, Ohio 44074, USA. email: charles@freude.com. home phone: 440 774 1926. professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.oberlin.net/~cwells/index.html NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm