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. © 2009 Springer Science + Business Media B.V.

Pre-torsors and Galois comodules over mixed distributive laws

MENINI, Claudia
Ultimo
2011

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. © 2009 Springer Science + Business Media B.V.
2011
Bohm, G.; Menini, Claudia
File in questo prodotto:
File Dimensione Formato  
Pre-torsors and Galois Comodules Over Mixed Distributive Law.pdf

solo gestori archivio

Descrizione: versione editoriale
Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 685.49 kB
Formato Adobe PDF
685.49 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
0806.1212.pdf

accesso aperto

Descrizione: versione pre print
Tipologia: Pre-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 397.82 kB
Formato Adobe PDF
397.82 kB Adobe PDF Visualizza/Apri

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/530064
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact