I have followed Travis' suggestion and been inspired by both answers and now have a working first version. This is wonderful!
Can I make two comments? i. I think it would be better to say that (to a first approximation) a sage category is a subcategory of Sets. When you are taught category theory it is drilled into you not to think of an object as a set. ii. I think this highlights the difference in the way the category/parent/framework is thought about and used in the two communities of algebraic geometry/commutative algebra and combinatorics. Just to clarify; I refer to tableaux because I am taking constructions that are well know for tableaux and generalising. One example is oscillating tableaux; these are sequences of partitions where you add or remove a single box at each step. One example I want to experiment with is vacillating tableaux. Then we have alternating tableaux, ribbon tableaux, ... I have a Tableaux parent and an element is a Tableau. A Tableau is mathematically a list of partitions and the class derives from CloneableArray (which has Element buried in it). I don't know how Morphisms, coercions etc. fit in here. So far, I have not had any use for them and I don't see them in examples. -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/d/optout.
