[Haskell-cafe] Re: categories and monoids

Conal Elliott conal at conal.net
Wed Mar 18 10:46:39 EDT 2009

So a clearer reframing might be: “Ring is like Field, but without
multiplicative inverse”.

On Wed, Mar 18, 2009 at 7:17 AM, Kalman Noel <noel.kalman at googlemail.com>wrote:

> 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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