A commutative algebra over a field naturally defines a representation of the category of finite sets and surjective maps. The restriction of this representation to the subcategory of sets of cardinality at most r is considered. For each r, two non-isomorphic algebras that define isomorphic representations of this subcategory are presented.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 492, 2021, pp. 149–156.
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Podkorytov, S.S. On the Algebra of the Möbius Crown. J Math Sci 264, 96–101 (2022). https://doi.org/10.1007/s10958-022-05981-y
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DOI: https://doi.org/10.1007/s10958-022-05981-y