On Tuesday 12 Jul 2011 12:16:04 Bertfried Fauser wrote: > Indeed a set itself can be seen as a category, as also a poset (with > greater effect), > functors are then just mappings. This point of view unites some > constructions. The > main problem I see, is how a CAS would `reason' about categorical > statements. A commutative diagram is just an equation of some (strict) > arrows, but you want to use properties of arrows, like monic, epic, or > being a kernel or an equalizer (in general limits and colimits, unique > arrows such as terminal and initial arros etc.)
I was wondering if there is some way to codify the mapping of the bottom-up description of a concrete category to its universal constructions. For instance, if we start with a finite set we might have: monic functor -> injective mapping epi functor -> surjective mapping Terminal Object -> singleton set Initial Object -> empty set Product -> Cartesian product Sum -> disjoint union ... Then if we have say, a set with a special element, there would be some other mapping and another for a set+binary operation and so on for every combination. I don't know how this would be codified but it just seems that if human practitioners of category theory can do this intuitively then there must be some hidden set of rules? Anyway, thanks for this, there are lots of things here for me to think about and I will follow up on the links you mentioned. Martin -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
