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- W2023386710 abstract "H. P. Gumm and T. Schröder stated a conjecture that the preservation of preimages by a functor T for which |T1| = 1 is equivalent to the satisfaction of the class equality $${{mathcal {HS}}({sf K}) = {mathcal {SH}}({sf K})}$$ for any class K of T-coalgebras. Although T. Brengos and V. Trnková gave a positive answer to this problem for a wide class of Set-endofunctors, they were unable to find the full solution. Using a construction of a rigid unary algebra we prove $${{mathcal {HS}} neq {mathcal {SH}}}$$ for a class of Set-endofunctors not preserving non-empty preimages; these functors have not been considered previously." @default.
- W2023386710 created "2016-06-24" @default.
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- W2023386710 date "2011-02-01" @default.
- W2023386710 modified "2023-10-17" @default.
- W2023386710 title "Rigidity of unary algebras and its application to the $${mathcal {HS} = mathcal {SH}}$$ problem" @default.
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- W2023386710 doi "https://doi.org/10.1007/s00012-011-0118-3" @default.
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