[Haskell-cafe] Re: categories and monoids

[Kalman Noel]

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.