Mathematics – Rings and Algebras
Scientific paper
2008-06-06
Appl. Categ. Structures 19 (2011), no. 3, 597-632
Mathematics
Rings and Algebras
34 pages LaTeX file. v2: a few typos corrected
Scientific paper
10.1007/s10485-008-9185-9
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 $(R_A,\xi)$ from some equalizer preserving comonad ${\mathbb C}$ to $N_BR_B$ 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.
Böhm Gabriella
Menini Claudia
No associations
LandOfFree
Pre-torsors and Galois comodules over mixed distributive laws does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pre-torsors and Galois comodules over mixed distributive laws, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pre-torsors and Galois comodules over mixed distributive laws will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-173242