On 5 April 2015 at 04:49, Ralf Hemmecke <[email protected]> wrote: > ... > In general I agree with Waldek that categories shouldn't have too many > requirements for their arguments. And as for Eltable(A,B), yes, > mathematically it sounds a bit odd that one can have a function > > elt: (%, A) -> B > > even though one doesn't know whether the elements of A can be > distinguished via equality or not.
The function 'elt' itself is not so strange, but what it claims to represent might be. The existence of 'elt' is supposed to mean that a value from the domain % (i.e. any domain which satisfies 'Eltable(A,B)') can be viewed as representing a function A->B. > But on the other hand, look at a > monoid M. It can be considered as a category with just one object X, > where the morphisms are the elements of M. Bill knows certainly enough > category theory to see that there is no need for equality on X to know > what the arrow > > m: X -> X (m \in M) > > is. I am not sure whether or not you are being serious here. There is certainly a need for equality on morphisms. You are right that mathematical category theory does not assume any structure on objects. But I do not see what point you are making. Do you imagine that there is some application of the FriCAS cateogry 'Eltable' independent of how it might be used in a domain? -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
