# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

1. Page created, but author did not leave any comments.

Anonymous

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 11th 2022

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 11th 2022

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.