Related papers: Simplicial Databases
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abstract homotopy theory, and computer science. Previous work…
We posit that striving for distributed systems that provide "single system image" semantics is fundamentally flawed and at odds with how systems operate in the physical world. We realize the database as an optimization of this system: a…
We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema.…
Database system is an indispensable part of software projects. It plays an important role in data organization and storage. Its performance and efficiency are directly related to the performance of software. Nowadays, we have many general…
We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graph homomorphism it is possible to build a basic query-answering mechanism based on semantic search. Graph homomorphism defines a partial order…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
We introduce indexing of tables referencing complex structures such as digraphs and spatial objects, appearing in genetics and other data intensive analysis. The indexing is achieved by extracting dimension schemas from the referenced…
We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…
Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids. In particular, we show that the usual model category structure on the category of simplicial…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue…
In the burgeoning era of big data, selecting the optimal database solution has become a critical decision for organizations across every industry. Big data demands a powerful database solution. Traditionally, SQL Database, Database ruled,…
We introduce a general abstract framework for database repairs, where the repair notions are defined using formal logic. We distinguish between integrity constraints and so-called query constraints. The former are used to model consistency…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
Large databases are often organized by hand-labeled metadata, or criteria, which are expensive to collect. We can use unsupervised learning to model database variation, but these models are often high dimensional, complex to parameterize,…
In the article Categorical Construction of Schemes, arXiv:2511.03433 we gave a natural definition of ordinary schemes based on the fact that the localization of a ring in a maximal ideal is a local representation of the corresponding…
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
We consider the evaluation of first-order queries over classes of databases that have bounded degree and low degree. More precisely, given a query and a database, we want to efficiently test whether there is a solution, count how many…
In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the…