Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
This does not look right: A “super commutative monoid” must involve a sign when two odd elements are commuted. Even if it’s just a graded monoid, then the degrees must add under the monoid operation, so that an even with an odd element gives an odd element.
So if “super commutative monoid” here is meant as a more primitive notion of “super vector space”, then for the terminology to be justified the entry must consider some kind of non-trivially symmetric braided tensor product on these gadgets.
Compare to super vector spaces: These are indeed just $\mathbb{Z}/2$-graded vector spaces in themselves, but get to be called “super” IFF regarded as objects in the non-trivial symmetric monoidal category structure on $\mathbb{Z}/2$-graded vector spaces. If that non-trivial symmetric braiding is not invoked, then $\mathbb{Z}/2$-graded vector spaces are just $\mathbb{Z}/2$-graded vector spaces and not super vector spaces. The same holds for their underlying additive monoids.
1 to 3 of 3