I am not quite sure what you mean by "inherit" in
this context, but at least in one sense you are not correct when you
say that AbelianMonoidRing does not inherit from Ring anymore.

58 +    if R has Ring then Ring

Well you know what I meant. If a (Abelian)MonoidRing is only a ring under certain conditions, then I find that confusing.

2) Up to minor details AbelianMonoidRing is in fact a specialization of
MonoidRingCategory, i.e. AbelianMonoidRing could inherit from
MonoidRingCategory.

Perhaps. But as mathematical abstractions I think these FriCAS
categories remain quite different in intention.

What do you think is the different intention?

In AbelianMonoidRing(R,E) the E is an additively written monoid. In MonoidRingCategory(R,M), M is multiplicatively written and not necessarily commutative. So what is the big difference?

Ralf

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