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    Anonymous

    v1, current

    • 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 /2\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 /2\mathbb{Z}/2-graded vector spaces. If that non-trivial symmetric braiding is not invoked, then /2\mathbb{Z}/2-graded vector spaces are just /2\mathbb{Z}/2-graded vector spaces and not super vector spaces. The same holds for their underlying additive monoids.

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