Pre-torsors and Galois comodules over mixed distributive laws

Gabriella Böhm, Claudia Menini

Research output: Contribution to journalArticle

2 Citations (Scopus)

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, RA) and (NB, RB) on one hand, and the category of regular comonad arrows (RA, ξ) from some equalizer preserving comonad ℂ to NBRB 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 D and a coregular comonad arrow from D to NARA, such that the comodule categories of ℂ and D are equivalent.

Original languageEnglish
Pages (from-to)597-632
Number of pages36
JournalApplied Categorical Structures
Volume19
Issue number3
DOIs
Publication statusPublished - Jun 1 2011

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Keywords

  • (Co)monad
  • Galois functor
  • Pre-torsor

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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