The {{mathcal {HS}} = {mathcal {SH}}} problem for coalgebras |
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| Authors: | Tomasz Brengos Věra Trnková |
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| Affiliation: | 1. Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661, Warszawa, Poland
2. Math. Institute of Charles University, Sokolovska 83, 18675, Praha 8, Czech Republic
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| Abstract: | H. P. Gumm and T. Schröder stated a hypothesis that the preservation of preimages by a functor T for which |T1| = 1 is equivalent to the satisfaction of the class equality ${{mathcal {HS}}(tt {K}) = {mathcal {SH}}(tt {K})}$ for any class K of T-coalgebras. Although we were not able to find a full solution, our paper gives a positive answer to this problem for a very wide class of Set-endofunctors. |
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