I have a somewhat related question about combinatorial species. A combinatorial species is really a functor from the category of finite set with bijections to the same category.
Let F be such a species. Currently (in Sage) we have that F.structures(someListOfLabels) gives an iterator over the resulting set of so-called structures and there is a method someStructure.change_labels(newListOfLabels) that returns the structure obtained by relabeling someStructure. More formally, let phi be the bijection phi: someListOfLabels -> newListOfLabels phi(someListOfLabels[i]) = newListOfLabels[i] then someStructure.change_labels(newListOfLabels) yields F[phi] (someStructure). Question: I wonder whether it would be better to go closer to the mathematics. For example, considering the species of cycles, shouldn't Cycles(listOfLabels) return the structures, and Cycles(someBijection) return an appropriate bijection? How are functors viewed in Sage currently? Martin -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
