On Aug 24, 5:33 am, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr> wrote: > - The problem with the map a -> (a,0) is only that 1_A is mapped to > (1_A,0) which is not 1_{A\oplusB} = (1_A,1_B), right? > > Otherwise said, the category of NonUnitalAlgebras (which is not yet > implemented in Sage) indeed has a direct sum?
I don't think so, but I could be wrong. There are maps of nonunital algebras from each of A and B to A \oplus B, but I don't think A \oplus B has the correct universal property: given ring maps f:A --> C and g: B --> C, you want a map h: A \oplus B --> C compatible with f, g, and the inclusions of A, B into A \oplus B. Since (a,b) = (a,0) + (0,b), I think the only way to define h is as h (a,b) = f(a) + g(b). But this isn't compatible with the product structure: in general, h((a1,b1) (a2, b2)) != h(a1,b1) h(a2,b2). Either that, or I'm being completely silly (or cocompletely silly, since we're talking about coproducts). Regards, John --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---