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Related papers: A Topology for Galois Types in AECs

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We study algebraic and topological properties of subsets of preorders on a group. In particular we study properties of the composition of two preorders, generalize a topological theorem of \cite{S} in the case of standard orders and show…

Group Theory · Mathematics 2021-02-17 Julie Decaup

We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…

Rings and Algebras · Mathematics 2023-04-18 Amartya Goswami

We present and characterize the classes of Grothendieck toposes having enough supercompact objects or enough compact objects. In the process, we examine the subcategories of supercompact objects and compact objects within such toposes and…

Category Theory · Mathematics 2021-01-12 Morgan Rogers

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

Algebraic Topology · Mathematics 2016-12-16 Sinan Yalin

We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…

Algebraic Topology · Mathematics 2021-07-23 Ashleigh Thomas , Kathleen Bates , Alex Elchesen , Iryna Hartsock , Hang Lu , Peter Bubenik

We investigate existentially closed models (of a quite arbitrary theory) equipped which an action of a fixed group G. We embed these structures in a monster model D of some well-rounded theory and describe them as PAC substructures of D.…

Logic · Mathematics 2019-05-24 Daniel Max Hoffmann

In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions of S-site and of model site, and the associated categories…

Algebraic Geometry · Mathematics 2007-05-23 Bertrand Toen , Gabriele Vezzosi

We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…

Logic in Computer Science · Computer Science 2025-11-24 Benjamin Przybocki , Guilherme V. Toledo , Yoni Zohar

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

Representation Theory · Mathematics 2015-01-27 Yuriy A. Drozd , Vasyl V. Zembyk

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…

Rings and Algebras · Mathematics 2007-11-26 Jose Gomez-Torrecillas , Joost Vercruysse

We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…

Artificial Intelligence · Computer Science 2025-08-13 Sridhar Mahadevan

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…

Machine Learning · Computer Science 2026-01-16 Bastian Rieck

We elaborate on the representation theorems of topoi as topoi of discrete actions of various kinds of localic groups and groupoids. We introduce the concept of "proessential point" and use it to give a new characterization of pointed Galois…

Category Theory · Mathematics 2007-05-23 Eduardo J. Dubuc

This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…

Category Theory · Mathematics 2026-03-02 Ismael Gutierrez Garcia , Luz Adriana Mejía Castaño

One of the main themes of this long article is the study of projective varieties which are K(H,1)'s, i.e. classifying spaces BH for some discrete group H. After recalling the basic properties of such classifying spaces, an important class…

Algebraic Geometry · Mathematics 2015-07-03 Fabrizio Catanese

We develop a notion of forking for Galois-types in the context of Abstract Elementary Classes (AECs). Under the hypotheses that an AEC $K$ is tame, type-short, and failure of an order-property, we consider {\bf Definition.} Let $M_0 \prec…

Logic · Mathematics 2017-01-06 Will Boney , Rami Grossberg

The sets of primitive foms may be decomposed into some Galois conjugacy classes. The purpose of this paper is to write down all of such classes with cardinal 1 or 2, explicitly in terms of some Eisenstein series, for level 1,2,3,4,6,8,9.…

Number Theory · Mathematics 2011-12-30 Saito Hayato , Suda Tomohiko

We make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable…

Logic · Mathematics 2021-05-28 Omar Leon Sanchez , David Meretzky , Anand Pillay

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

Logic · Mathematics 2024-06-12 Niels Charlier , Hans Vernaeve

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:…

Number Theory · Mathematics 2020-06-11 David Harbater , Pierre Dèbes
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