caa a22 4500 445378867 CHVBK 20180317143011.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10485-008-9185-9 doi (NATIONALLICENCE)springer-10.1007/s10485-008-9185-9 Pre-torsors and Galois Comodules Over Mixed Distributive Laws [Elektronische Daten] [Gabriella Böhm, Claudia Menini] We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions (N A,R A) and (N B,R B) on one hand, and the category of regular comonad arrows (R A,ξ) from some equalizer preserving comonad ${\mathbb C}$ to N B R B on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras. Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad ${\mathbb D}$ and a co-regular comonad arrow from ${\mathbb D}$ to N A R A, such that the comodule categories of ${\mathbb C}$ and ${\mathbb D}$ are equivalent. Springer Science+Business Media B.V., 2009 (Co)monad nationallicence Galois functor nationallicence Pre-torsor nationallicence Böhm Gabriella Research Institute for Particle and Nuclear Physics, P.O.B.49, 1525 Budapest 114, Budapest, Hungary aut Menini Claudia Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy aut Applied Categorical Structures Springer Netherlands 19/3(2011-06-01), 597-632 0927-2852 19:3<597 2011 19 10485 https://doi.org/10.1007/s10485-008-9185-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-008-9185-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Böhm Gabriella Research Institute for Particle and Nuclear Physics, P.O.B.49, 1525 Budapest 114, Budapest, Hungary aut NATIONALLICENCE 700 1- Menini Claudia Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/3(2011-06-01), 597-632 0927-2852 19:3<597 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer