Am Mittwoch, 18. März 2009 05:36 schrieb wren ng thornton: > Wolfgang Jeltsch wrote: > > Am Dienstag, 17. März 2009 10:54 schrieben Sie: > > > I'm reading the Barr/Wells slides at the moment, and they say the > > > following: > > > > > > "Thus a category can be regarded as a generalized monoid, > > > > What is a “generalized monoid”? According to the grammatical construction > > (adjective plus noun), it should be a special kind of monoid, like a > > commutative monoid is a special kind of monoid. But then, monoids would > > be the more general concept and categories the special case, quite the > > opposite of how it really is. > > Usually in math texts "a Y is a generalized X" means exactly "Ys are a > generalization of Xs", and thus Y is the larger class of objects got by > relaxing some law in X. It's a description, not a name. E.g. Hilbert > space is a generalized Euclidean space, Heyting algebras are generalized > Boolean algebras, modules are generalized vector spaces, etc.
I know these phrases but I always considered them as something, mathematicians use when they talk to each other informally, not what they would write in a book. Best wishes, Wolfgang _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
