Related papers: Simplicial Databases
In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and…
A class of relational databases has low degree if for all $\delta>0$, all but finitely many databases in the class have degree at most $n^{\delta}$, where $n$ is the size of the database. Typical examples are databases of bounded degree or…
Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…
In this article, we define two equivalent new model structures on $\mathbf{sCat}$ the category of simplicial objects in $\mathbf{Cat}$. Then we construct the corresponding stable model category of spectra $Sp(\mathbf{sCat})$ and make some…
The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest.…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
Model theory was born and developed as a part of mathematical logic. It has various application domains but is not beholden to any of them. A priori, the research area known as finite model theory would be just a part of model theory but…
A simplicial set is said to be non-singular if its non-degenerate simplices are embedded. Let $sSet$ denote the category of simplicial sets. We prove that the full subcategory $nsSet$ whose objects are the non-singular simplicial sets…
The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is…
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the…
Summarizing topological information from datasets and maps defined on them is a central theme in topological data analysis. \textsf{Mapper}, a tool for such summarization, takes as input both a possibly high dimensional dataset and a map…
As information becomes increasingly sizable for organizations to maintain the challenge of organizing data still remains. More importantly, the on-going process of analysing incoming data occurs on a continual basis and organizations should…
Table learning, which lies at the intersection of machine learning and modern database systems, has recently attracted growing attention. However, existing table learning frameworks typically require explicit data export and extensive…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
As the use of technology increases and data analysis becomes integral in many businesses, the ability to quickly access and interpret data has become more important than ever. Information retrieval technologies are being utilized by…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…
The rise of Large Language Models (LLMs) has accelerated the long-standing goal of enabling natural language querying over complex, hybrid databases. Yet, this ambition exposes a dual challenge: reasoning jointly over structured,…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
The development of Natural Language Interfaces to Databases (NLIDBs) has been greatly advanced by the advent of large language models (LLMs), which provide an intuitive way to translate natural language (NL) questions into Structured Query…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…