0*1 = 0 - Category Theory

What's the name of the structure which has an element that absorbs the others like 0*1 = 0 ?

@Bolt Monoid?

Monoid only have an identity object which is 1 in the case of the monoid (a, *, 1), right?

what is the structure (a, *, 1, 0) where 1 is the identity object and 0 the absorbing object?

Oh, sorry, now I see what you mean :sweat_smile:

I'm not aware of a special name for the structure, it will just be a semigroup or whatever with an absorbing element

oh okay! Thanks :P

Would something like

absorbingElement :: (Num a, Monoid a) => a
absorbingElement = mempty - mempty

be a good approach?

@Bolt Theoretically, nothing is stopping me from implementing NonZero type and giving it Num and Monoid instance, does it?

you're right :frown:

I'll just go with this approach: http://hackage.haskell.org/package/zero-0.1.5/docs/Data-Zero.html

@Bolt I've sometimes seen that called an "annihilating element"

You might be looking for a ring or some slight weakening/strengthening of that concept

@Bolt I think the literature calls that a "monoid with zero", but that's equivalent to "monoid with absorbing element" or "monoid with annihilator"

Yes, I found semigroups with zero

Category Theory is a trivial Category Theory

@Emily Pillmore I guess "Abstract" in that topic name is not "abstract" enough for this comment :smiley:

just upon the concept of a near-semiring, which is equipped with an absorbing element, in case that helps