Category of Abelian monoids


Cat::AbelianMonoid represents an Abelian monoid.

An Cat::AbelianMonoid is an Abelian semi-group with a neutral element dom::zero according to the operation + (_plus).

Use the axiom Ax::normalRep to state that zero is always represented in a unique way (i.e. canonically).

If an Abelian monoid has not the axion Ax::normalRep then dom::zero is only one possible representation of the neutral element. An Abelian semi-group must at least have the method "iszero" to test for zero in such a case.


If the domain has Ax::canonicalRep, then Ax::normalRep.



Must hold the neutral element according to the operation +.


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