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Anonymouse

]]>Thanks to a reference provided by Rod McGuire in another thread (here):

- F. William Lawvere:
*The legacy of Steve Schanuel!*(2015) [web]

we can settle the question of origin of the terminology ’rig’ – because Lawvere writes there, about his work with Schanuel, that:

We were amused when we finally revealed to each other that we had each independently come up with the term ’rig’.

Have added this to the entry.

]]>Thanks, I have added that to the entry.

]]>It appears earlier than 1992, e.g., in

- S.H. Schanuel, Negative sets have Euler characteristic and dimension, in: Proceedings of Category Theory, Como, Italy,1990, in: Lecture Notes in Mathematics, vol. 1488, Springer-Verlag, 1991, pp. 379–385.

See here, page 379. But I wouldn’t bet this is the earliest appearance either.

]]>added pointer to

- William Lawvere, pp. 1 of:
*Introduction to Linear Categories and Applications*, course lecture notes (1992) [pdf]

Is this (on p. 2) maybe the actual origin of the term “rig”?

]]>Added a reference to Rig

]]>adding paragraph on the relationship between rigs and semirings.

Anonymous

]]>*define a ring to be a monoid object in the category of abelian groups

]]>I’ve seen four different definitions of a “semiring” out there, depending on the author:

- A semigroup object in the category of commutative semigroups
- A monoid object in the category of commutative semigroups
- A semigroup object in the category of commutative monoids
- A monoid object in the category of commutative monoids

The problem is already there in the definition of a ring, as some authors define a ring to be a semigroup object in the category of abelian groups, while other authors define a ring to be a monoid object in the category of commutative monoids

]]>Thank you, it seems very logical to me now. I will use the term rig for the structure with the two identities from now on.

]]>The same is true of Kazimierz Glazek’s *A guide to the literature on semirings and their applications in mathematics and information sciences*

Semirings as defined on Wolfram MathWorld don’t have either an additive or multiplicative identity; they are semigroup objects in the category of commutative semigroups.

]]>Added link to “multiplicatively cancellable semi-ring”.

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