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1. • CommentRowNumber1.
   • CommentAuthorbblfish
   • CommentTimeSep 5th 2019
   • (edited Sep 5th 2019)
   • PermaLink
   Author: bblfish
   Format: MarkdownItexI have come across a couple of very intriguing papers by David I Spivak, that make category theory incredibly relevant to use in databases, and so provide a great way to use widely understood concepts to understand ones in Cats. In the 2012 paper "[Functorial Data Migration](https://www.sciencedirect.com/science/article/pii/S0890540112001010)" the case is made that small categories can be seen as schemas, and functors from those to Set (to start with), form DB instances. The examples there are very clear. What is interesting is that they show how via a Grothendieck construction one can translate any database into an RDF Graph and back. I had [mentioned in a post here 5 years ago](https://nforum.ncatlab.org/discussion/6185/the-category-of-resource-description-framework-rdf/) an earlier thesis by Benjamin Braatz that gave a Cats view of RDF. What is very intruiging about this view is its generality, so that it should be very interesting to people here. From that paper I was lead to another came out the same year [Database Queries and Constraints via Lifting Problems](https://arxiv.org/pdf/1202.2591.pdf) where Spivak also looks at SPARQL (the RDF query language). I have not yet finished this. For a question on RDF and Institution Theory with further pointers see the question on Stack Exchange [What does the category of RDF Models look like in Institution Theory](https://cstheory.stackexchange.com/questions/41578/what-does-the-category-of-rdf-models-look-like-in-institution-theory).

   I have come across a couple of very intriguing papers by David I Spivak, that make category theory incredibly relevant to use in databases, and so provide a great way to use widely understood concepts to understand ones in Cats.

   In the 2012 paper “Functorial Data Migration” the case is made that small categories can be seen as schemas, and functors from those to Set (to start with), form DB instances. The examples there are very clear. What is interesting is that they show how via a Grothendieck construction one can translate any database into an RDF Graph and back. I had mentioned in a post here 5 years ago an earlier thesis by Benjamin Braatz that gave a Cats view of RDF. What is very intruiging about this view is its generality, so that it should be very interesting to people here.

   From that paper I was lead to another came out the same year Database Queries and Constraints via Lifting Problems where Spivak also looks at SPARQL (the RDF query language). I have not yet finished this.

   For a question on RDF and Institution Theory with further pointers see the question on Stack Exchange What does the category of RDF Models look like in Institution Theory.