[microsound] category theory and composition

[Andrew Salch]

On Tue, 22 Dec 2009, Justin Glenn Smith wrote:
> But I was thinking about a context in which this could be made a true 
> statement. In category theory there is the concept of a functor, which 
> is a structure-preserving mapping from one category to another. If we 
> treated two genres of composition as categories, we could define a 
> functor to take a composition in one of these genres and get a 
> composition in the other, without losing structural information (ie. 
> analogous patterns would exist).


How do we regard a genre of composition as a category? What are the 
objects and the morphisms of a genre of composition?