Category theory for computing science
Category theory for computing science
Basic category theory for computer scientists
Basic category theory for computer scientists
Data modeling from a categorical perspective
Data modeling from a categorical perspective
Deciding type equivalence in a language with singleton kinds
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On category theory as a (meta) ontology for information systems research
Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
Categorical Models of Relational Databases I: Fibrational Formulation, Schema Integration
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Storage and Querying of E-Commerce Data
Proceedings of the 27th International Conference on Very Large Data Bases
A Category-theoretic Account of Program Modules
Category Theory and Computer Science
A Calculus for Collections and Aggregates
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
On the Value of Commutative Diagrams in Information Modelling
AMAST '93 Proceedings of the Third International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Relational lenses: a language for updatable views
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Memory Evolutive Systems; Hierarchy, Emergence, Cognition (Studies in Multidisciplinarity)
Memory Evolutive Systems; Hierarchy, Emergence, Cognition (Studies in Multidisciplinarity)
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data types as initial algebras: A unification of Scottery and ADJery
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Conceptual Mathematics: A First Introduction to Categories
Conceptual Mathematics: A First Introduction to Categories
Polymorphic abstract syntax via Grothendieck construction
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Category Theory
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
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In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three ''data migration functors'', which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language. We begin the paper with a multitude of examples to motivate the definitions, and near the end we provide a dictionary whereby one can translate database concepts into category-theoretic concepts and vice versa.