Nicolas, There needs to be some serious thought about computability in Hom categories.. In what categories can one automatically compute the inverse of an invertible map, tell whether a morphism is zero, optimize composition of morphisms, etc. The TestSuites should be smart enough to automatically reflect this.
I am coming around to the viewpoint that one should almost never need to use "orphan" functions. (Yet I have been using a lot of them for doctests in new smash product code, where the required actions are not necessarily already incorporated into existing objects). For identity morphisms, one can define a single global "_the_id" identity pure function and have everyone's identity morphism wrap it by calling SetMorphism. It passes pickling, is as cheap as possible, and provides identity morphisms, which, for categorical and other reasons, are needed. But the right solution is to do the same thing but "officially" by strengthening the Hom code to supply identity morphisms and their properties. Implementation of categories should be enhanced to have special objects such as identity objects. So when you get around to messing with Homs, please add identity morphisms as category-flavored wrappers around a single little pure identity function, and the knowledge to the Hom code that the identity morphism composes trivially. --Mark -- You received this message because you are subscribed to the Google Groups "sage-devel" 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/sage-devel. For more options, visit https://groups.google.com/d/optout.
