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 Sibirsk. Mat. Zh., 2013, Volume 54, Number 5, Pages 1087–1101 (Mi smj2479)

Liftings of normal functors in the category of compacta to categories of topological algebra and analysis

O. R. Nykyforchyna, D. Repovšbc

a Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
b Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
c University of Ljubljana, Ljubljana, Slovenia

Abstract: We prove that the liftings of a normal functor $F$ in the category of compact Hausdorff spaces to the categories of (abelian) compact semigroups (monoids) are determined by natural transformations $F(-)\times F(-)\to F(-\times-)$ satisfying requirements that correspond to associativity, commutativity, and the existence of a unity. In particular, the tensor products for normal monads satisfy (not necessarily all) these requirements.
It is proved that the power functor in the category of compacta is the only normal functor that admits a natural lifting to the category of convex compacta and their continuous affine mappings.

Keywords: compact semigroup, compact monoid, convex compactum, normal functor, lifting.

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English version:
Siberian Mathematical Journal, 2013, 54:5, 871–882

Bibliographic databases:

Document Type: Article
UDC: 515.12

Citation: O. R. Nykyforchyn, D. Repovš, “Liftings of normal functors in the category of compacta to categories of topological algebra and analysis”, Sibirsk. Mat. Zh., 54:5 (2013), 1087–1101; Siberian Math. J., 54:5 (2013), 871–882

Citation in format AMSBIB
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