Related papers: On covering theory and its applications

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…

Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.

Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as…

In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties. For each category $\mathcal{C}$ of…

In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.

The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal…

We study pullback from a topological viewpoint with emphasis on pullback of covering maps. We generalize a triad of Quillen on properties of the pullback functor.

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…

We consider function fields of transcendence degree at least 2 over algebraic closures of finite fields, and describe a functorial way to recover such function fields form their pro-l Galois theory.

We introduce the notion of Krull super-dimension of a super-commutative super-ring. This notion is used to describe regular super-rings and calculate Krull super-dimensions of completions of super-rings. Moreover, we use this notion to…

Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…

Let R be a complete discrete valuation ring of mixed characteristics, with algebraically closed residue field k. We study the existence problem of equivariant liftings to R of Galois covers of nodal curves over k. Using formal geometry, we…

We study the model theory of covers of groups definable in o-minimal structures. This includes the case of covers of compact real Lie groups. In particular we study categoricity questions, pointing out some notable differences with the case…

We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…

The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…

Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as…

While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…

This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open questions. We illustrate important phenomena which occur for…

We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…

We develop a Galois (descent) theory for comonads within the framework of bicategories. We give generalizations of Beck's theorem and the Joyal-Tierney theorem. Many examples are provided, including classical descent theory, Hopf-Galois…