Geodesic
On the algebra of the M\"obius crown
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 149-156

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A commutative algebra over a field gives rise to a representation of the category of finite sets and surjective maps. We consider the restriction of this representation to the subcategory of sets of cardinality at most $r$. For each $r$, we present two non-isomorphic algebras that give rise to isomorphic representations of this subcategory. 
@article{ZNSL_2020_492_a10,
     author = {S. S. Podkorytov},
     title = {On the algebra of the {M\"obius} crown},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--156},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a10/}
}
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S. S. Podkorytov. On the algebra of the M\"obius crown. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 149-156. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a10/