Related papers: On the relationship between Galois and Tannakian c…

Strong similarities have been long observed between the Galois (Categories Galoisiennes) and the Tannaka (Categories Tannakiennes) theories of representation of groups. In this paper we construct an explicit (neutral) Tannakian context for…

Galois categories can be viewed as the combinatorial analog of Tannakian categories. We introduce the notion of pre-Galois category, which can be viewed as the combinatorial analog of pre-Tannakian categories. Given an oligomorphic group…

The main result of this thesis is the construction of a tannakian context over the category of sup-lattices, associated with an arbitrary Grothendieck topos, and the attainment of new results in tannakian representation theory from it.…

We describe the origins of the theory of tannakian categories, and summarize its main results.

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…

A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…

We give a detailed proof of Kolchin's results on differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. We closely follow former works due to Pillay and…

We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…

Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these…

We introduce the existence of a Genus-Type Theory that generalizes classical genus theory by linking fractional ideals of number fields to structures built from their Galois groups and associated Diophantine equations, as formally stated in…

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

We develop a theory of tensor categories over a field endowed with abstract operators. Our notion of a "field with operators", coming from work of Moosa and Scanlon, includes the familiar cases of differential and difference fields,…

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the…

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…

We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…

In the context of a tower of (strongly Birkhoff) Galois structures in the sense of categorical Galois theory, we show that the concept of a higher covering admits a characterisation which is at the same time absolute (with respect to the…

In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose…

This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. The fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. For a linear equations with respect to…

We introduce and study a class of field extensions that we call pre-Galois; viz. extensions that become Galois after some linearly disjoint Galois base change. Among them are geometrically Galois extensions of k(T), with k a field:…