On Thu, Mar 19, 2009 at 5:43 AM, Wolfgang Jeltsch <[email protected]> wrote: > Am Mittwoch, 18. März 2009 15:17 schrieben Sie: >> Wolfgang Jeltsch schrieb: >> > Okay. Well, a monoid with many objects isn’t a monoid anymore since a >> > monoid has only one object. It’s the same as with: “A ring is a field >> > whose multiplication has no inverse.” One usually knows what is meant >> > with this but it’s actually wrong. Wrong for two reasons: First, because >> > the multiplication of a field has an inverse. Second, because the >> > multiplication of a ring is not forced to have no inverse but may have >> > one. >> >> “A ring is like a field, but without a multiplicative inverse” is, in my >> eyes, an acceptable formulation. We just have to agree that “without” >> here refers to the definition, rather than to the definitum. > > Note that you said: “A ring is *like* a field.”, not “A ring is a field.” > which was the formulation, I criticized above. >
"Alternatively, the fundamental notion of category theory is that of a monoid ... a category itself can be regarded as a sort of generalized monoid." -- Saunders MacLane, "Categories for the Working Mathematician" (preface) _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
