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triple; normal functor; category of algebras; distributive law; compact Hausdorff space; power functor; projective triple
We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.
[1] Barr M., Wells Ch.: Toposes, triples and theories. Springer-Verlag, 1985. MR 0771116 | Zbl 1081.18006
[2] Beck J.M.: Triples, algebras and cohomology. Ph.D. Thesis, Columbia University, 1967. Zbl 1022.18004
[3] Fedorchuk V.V.: Soft mappings, multivalued retractions and functors (in Russian). Uspekhi Mat. Nauk, no. 6, 41 (1986), 121-159. MR 0890495
[4] Fedorchuk V.V., Filippov V.V.: General Topology. Fundamental Constructions (in Russian). Izd-vo MGU, 1988.
[5] MacLane S.: Categories for Working Mathematician. Springer-Verlag 1971. MR 0354798
[6] Radul T.M.: On triples generated by some normal functors (in Ukrainian). Visn. Lviv. Un-tu. Ser. mekh.-mat., no. 34, 1990, 59-62. MR 1196681
[7] Shchepin E.V.: Functors and infinite powers of compacta (in Russian). Uspekhi Mat. Nauk, no. 3, 36 (1981), 3-62. MR 0622720
[8] Vinárek J.: Projective monads and extensions of functors. Math. Centr. Afd., no. 195, (1983), 1-12. MR 0733105
[9] Zarichnyĭ M.M.: Superextension triple and its algebras (in Russian). Ukr. Mat. Zh., no. 3, 39 (1987), 303-309. MR 0899494
[10] Zarichnyĭ M.M.: Multiplicative normal functor is a power one (in Russian). Mat. Zametki, no. 1, 41 (1987), 93-110. MR 0886172
[11] Zarichnyĭ M.M.: Profinite multiplicativity of functors and characterization of projective triples in the category of compacta (in Russian). Ukr. Mat. Zh., no. 9, 42 (1990), 1271-1275. MR 1093642
[12] Zarichnyĭ M.M.: On monadic functors of finite degree (in Russian). In: Questions of geometry and topology, Petrozavodsk, 1986. MR 0975510
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