Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

Michael M. Zarichnyi

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 785-790
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Zarichnyi, Michael M.. "Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 785-790. <http://eudml.org/doc/247293>.

@article{Zarichnyi1991,
abstract = {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.},
author = {Zarichnyi, Michael M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {triple; normal functor; category of algebras; distributive law; compact Hausdorff space; power functor; projective triple; normal functor; category of algebras; compact Hausdorff space; power functor; projective triple; distributive law},
language = {eng},
number = {4},
pages = {785-790},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras},
url = {http://eudml.org/doc/247293},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Zarichnyi, Michael M.
TI - Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 785
EP - 790
AB - 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.
LA - eng
KW - triple; normal functor; category of algebras; distributive law; compact Hausdorff space; power functor; projective triple; normal functor; category of algebras; compact Hausdorff space; power functor; projective triple; distributive law
UR - http://eudml.org/doc/247293
ER -

References

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  1. Barr M., Wells Ch., Toposes, triples and theories, Springer-Verlag, 1985. Zbl1081.18006MR0771116
  2. Beck J.M., Triples, algebras and cohomology, Ph.D. Thesis, Columbia University, 1967. Zbl1022.18004
  3. Fedorchuk V.V., Soft mappings, multivalued retractions and functors (in Russian), Uspekhi Mat. Nauk, no. 6, 41 (1986), 121-159. (1986) MR0890495
  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. MR0354798
  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. MR1196681
  7. Shchepin E.V., Functors and infinite powers of compacta (in Russian), Uspekhi Mat. Nauk, no. 3, 36 (1981), 3-62. (1981) MR0622720
  8. Vinárek J., Projective monads and extensions of functors, Math. Centr. Afd., no. 195, (1983), 1-12. (1983) MR0733105
  9. Zarichnyĭ M.M., Superextension triple and its algebras (in Russian), Ukr. Mat. Zh., no. 3, 39 (1987), 303-309. (1987) MR0899494
  10. Zarichnyĭ M.M., Multiplicative normal functor is a power one (in Russian), Mat. Zametki, no. 1, 41 (1987), 93-110. (1987) MR0886172
  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. (1990) MR1093642
  12. Zarichnyĭ M.M., On monadic functors of finite degree (in Russian), In: Questions of geometry and topology, Petrozavodsk, 1986. MR0975510

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