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- W3099931493 abstract "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." @default.
- W3099931493 created "2020-11-23" @default.
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- W3099931493 date "2009-01-22" @default.
- W3099931493 modified "2023-09-25" @default.
- W3099931493 title "Pre-torsors and Galois Comodules Over Mixed Distributive Laws" @default.
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- W3099931493 doi "https://doi.org/10.1007/s10485-008-9185-9" @default.
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