> A category in which Hom sets form abelian groups and in which you have > finite direct sums is an "additive category". An "abelian category" > is one in which, loosely speaking, you have well-behaved short exact > sequences: every monomorphism fits into a short exact sequence, and > every epimorphism fits into a short exact sequence. Wikipedia has a > reasonable definition, I think. > > The category of modules over any ring is abelian (but not just the > category of free modules, as someone has pointed out in > category_types.py, unless the ring is a field).
Thanks for the background. > > Note about the patch: to avoid dependencies on the inheritance order > > between the bases, wouldn't it be more natural to have the default > > definition of is_abelian in Category? > > That sounds like a good idea. Will do. > (Although should the default definition be "NotImplemented" or > "False"? I'm not sure.) Do we have a consensus for NotImplemented now? Cheers, Nicolas -- Nicolas M. ThiƩry "Isil" <nthi...@users.sf.net> http://Nicolas.Thiery.name/ --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---