Related papers: Higher internal covers
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
The correspondence between definable connected groupoids in a theory $T$ and internal generalised imaginary sorts of $T$, established by Hrushovski in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics, 2012], is…
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…
Tabular foundational models are pre-trained models designed for a wide range of tabular data tasks. They have shown strong performance across domains, yet their internal representations and learned concepts remain poorly understood. This…
We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We study thick subcategories defined by modules of complexity one in $\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.
In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of $4$d Chern-Simons theory with defects, which provided a…
In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic…
We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…
This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…
This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…
We introduce the notion of a higher covering diagram in a base $\infty$-category $\mathcal{C}$. The theory of higher covering diagrams in $\mathcal{C}$ will be shown to recover various descent conditions known from the $\infty$-categorical…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…