[Haskell-cafe] Re: categories and monoids
Wolfgang Jeltsch
g9ks157k at acme.softbase.org
Thu Mar 19 06:43:49 EDT 2009
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.
Best wishes,
Wolfgang
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