Functorial data migration

@article{Spivak2012FunctorialDM,
  title={Functorial data migration},
  author={David I. Spivak},
  journal={Inf. Comput.},
  year={2012},
  volume={217},
  pages={31-51}
}

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References

SHOWING 1-10 OF 94 REFERENCES
Categorical Models of Relational Databases I: Fibrational Formulation, Schema Integration
TLDR
This paper uses category theory to provide a formal mathematical framework for specifying and integrating relational database schemas, and shows how the process of schema integration and the resolution of conflicts between schemas may be carried out in a mathematically rigorous setting.
Relational lenses: a language for updatable views
TLDR
The approach is to define a bi-directional query language, in which every expression can be read bot(from left to right) as a view definition and (from right to left) as an update policy.
Simplicial Databases
TLDR
A category DB is defined, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps, and it is proved that limits and colimits always exist in DB and that they correspond to queries such as select, join, union, etc.
Data modeling from a categorical perspective
TLDR
The CGOOD model is introduced, a categorical graph-based data model based on category theory, a formalism that is especially useful for data modeling purposes because of its generic and fundamental character.
A Calculus for Collections and Aggregates
TLDR
A calculus that should play for database query languages the same role that the lambda calculus plays for functional programming, and a new concept: monads enriched with algebraic structure is introduced.
Ologs: A Categorical Framework for Knowledge Representation
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and
Storage and Querying of E-Commerce Data
TLDR
This work represents objects in a vertical format storing an object as a set of tuples, and creates a logical horizontal view of the vertical representation and transforms queries on this view to the vertical table.
Databases as Graphical Algebras: Algebraic Graph-Based Approach to Data Modeling and Database Design
TLDR
The approach is based on a graphical speciication language possessing formal semantics so that graphical images themselves are precise speciications suitable for implementation and provides the possibility of automated view integration and, correspondingly, automated database design.
Generic Model Management: A Database Infrastructure for Schema Manipulation
TLDR
The main concepts of model management are explained, some recent progress on model matching algorithms are reported, and a category-theoretic approach to a formal semantics for model management is sketched.
Databases as Diagram Algebras: Specifying Queries and Views Via the Graph-Based Logic of Sketches
TLDR
A formalized speciication framework for heterogeneous multibase systems can be built and the main technical contribution is the development of algebraic machinery for diagram operations including parsing of sketch terms.
...
...