categories: Re: Structure Preserving: Definition?

[Charles Wells <charles@freude.com>]

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
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