# Pre-torsors and equivalences

@inproceedings{Bhm2006PretorsorsAE, title={Pre-torsors and equivalences}, author={Gabriella B{\`o}hm and Tomasz Brzezinski}, year={2006} }

Properties of (most general) non-commutative torsors or A–B torsors are analysed. Starting with pretorsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is shown that a class of faithfully flat pre-torsors induces equivalences between categories of comodules of associated corings. It is then proven that A–B torsors correspond to monoidal functors (and, under some additional conditions, equivalences) between categories of comodules of…

## 5 Citations

Fiber functors, monoidal sites and Tannaka duality for bialgebroids

- Mathematics
- 2009

What are the fiber functors on small additive monoidal categories C which are not abelian? We give an answer which leads to a new Tannaka duality theorem for bialgebroids generalizing earlier results…

A Schneider type theorem for Hopf algebroids

- Mathematics
- 2006

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B ⊆ A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the…

Pre-torsors and Galois Comodules Over Mixed Distributive Laws

- Mathematics, Computer ScienceAppl. Categorical Struct.
- 2011

Developing a bi-Galois theory of comonads, it is shown that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad and a co-regular com onad arrow from NARA, such that the comodule categories of C and D are equivalent.

Bimodule herds

- Mathematics
- 2008

The notion of a bimodule herd is introduced and studied. A bimodule herd consists of a B-A bimodule, its formal dual, called a pen, and a map, called a shepherd, which satisfies unitality and…

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