Non-normal Galois theories and some resulting structures

Counting Hopf Galois Structures on Non-abelian Galois Field Extensions

Let L be a field which is a Galois extension of the field K with Galois group G. Greither and Pareigis [GP87] showed that for many G there exist K-Hopf algebras H other than the group ring KG which make L into an H-Hopf Galois extension of K (or a Galois H∗object in the sense of Chase and Sweedler [CS69]). Using Galois descent they translated the problem of determining the Hopf Galois structure...

t-Structures are Normal Torsion Theories

We characterize t-structures in stable∞-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure t on a stable∞-category C is equivalent to a normal torsion theory F on C, i.e. to a factorization system F = (E,M) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts. Introduction. The ide...

On Galois theories

The classical Galois theory of fields and the classification of covering spaces of a path-connected, locally path-connected, and semi-locally simply connected space (which will be referred to as the Galois theory of covering spaces) appear very similar. We study the connection of these two Galois theories by generalizing them in categorical language as equivalences of certain categories. This i...

Galois structures

Galois Functors and Entwining Structures

Galois comodules over a coring can be characterised by properties of the relative injective comodules. They motivated the definition of Galois functors over some comonad (or monad) on any category and in the first section of the present paper we investigate the role of the relative injectives (projectives) in this context. Then we generalise the notion of corings (derived from an entwining of a...