Cat::SemiRing – the category of semi-rings

Cat::SemiRing represents the category of semi-rings.

Categories

Cat::SemiRng, Cat::AbelianMonoid, Cat::Monoid

Details:

• A Cat::SemiRing is essentially a ring (Cat::Ring), except that the operation + (_plus) is not required to be invertible. In other words, this is an Abelian monoid according to the operation + and a non-Abelian monoid according to the operation * (_mult) where in addition the two distributive laws and hold.

• Note that a semi-ring without unit is a Cat::SemiRng.

Background:

A Cat::SemiRing is not quite a left module over itself since the category Cat::LeftModule requires the domain to be an Abelian group according to the operation + (_plus).