Related papers: Functorial Data Migration
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
In the current paper, we propose to fuse together stored data (tables) and their functional dependencies (FDs) inside a DBMS. We aim to make FDs first-class citizens: objects which can be queried and used to query data. Our idea is to allow…
We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint functors between corresponding copresheaf categories. These may…
Relational databases play a central role in many information systems. Their schema contains structural (e.g. tables and columns) and behavioral (e.g. stored procedures or views) entity descriptions. Then, just like for ``normal'' software,…
We investigate a possible category theoretical description for agent based modeling by outlining justifications for two main principles to describe the valuations in a realistic way in microeconomics: 1) It is assumed that the valuations…
In the paper a new approach to data representation and manipulation is described, which is called the concept-oriented data model (CODM). It is supposed that items represent data units, which are stored in concepts. A concept is a…
When a new programming language appears, the syntax and intended behaviour of its programs need to be specified. The behaviour of each language construct can be concisely specified by translating it to fundamental constructs (funcons),…
Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As…
Categorical Query Language is an open-source query and data integration scripting language that can be applied to common challenges in the field of computational science. We discuss how the structure-preserving nature of CQL data migrations…
A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type…
To any model category $\mathcal{M}$, we associate a modular model category, a functor of points $\mathcal{M}[-]:$ Cat $\rightarrow$ Cat, that associates to any small category $\mathcal{C}$ a functor category $\mathcal{M}[\mathcal{C}] =…
An alternative definition of the concept is given of functional dependence among the attributes of the relational schema in the Relational Model, this definition is obtained in terms of the set theory. For that which a theorem is…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
Functional Distributional Semantics is a recently proposed framework for learning distributional semantics that provides linguistic interpretability. It models the meaning of a word as a binary classifier rather than a numerical vector. In…
In this article we discuss an approach to database optimisation in which a conceptual schema is optimised by applying a sequence of transformations. By performing these optimisations on the conceptual schema, a large part of the database…
In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
In this paper we define a new algorithm to convert an input relational database to an output set of RDF triples. The algorithm can be used to e.g. load CSV data into a financial OWL ontology such as FIBO. The algorithm takes as input a set…
Database system architectures are undergoing revolutionary changes. Algorithms and data are being unified by integrating programming languages with the database system. This gives an extensible object-relational system where non-procedural…
We define the notion of linguistic structure on a small category, in order to provide a more formal description of ontology logs, also known as ologs, introduced by R. E. Kent and D. I. Spivak in their paper "Ologs: A categorical framework…