[Haskell-cafe] Re: categories and monoids
noel.kalman at googlemail.com
Wed Mar 18 10:17:14 EDT 2009
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.
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