I am aware of at least two different theoretical approaches for understanding relational databases: Codd's relational algebra/calculus, and category theory.
Is there any relationship between these two approaches? Are they in some sense equivalent? Is there any introductory work explaining how both of these frameworks explain relational databases?
Background: A while ago I read David Spivak's Category Theory for Scientists which spent quite some time discussing how category theory could be applied to understand the theory of relational databases. However, having little personal experience about what relational databases are or why they are useful, at the time I did not fully appreciate the depths of insight found in the book.
However, recently I have been learning about SQL queries and two R packages for data manipulation: dplyr and data.table. SQL can apparently express much of the ideas of Codd's relational algebra/calculus/model, but not all. Moreover, the author of dplyr, Hadley Wickham, has stated explicitly that his philosophy underlying the package is based on Codd's work on relational algebra, and the basic commands of data.table map fairly well to commands in SQL and dplyr.
I also know that category theory influences a lot of programmers using functional programming languages like Haskell. However, I am not really aware of there being any use of functional programming for data manipulation or data science, besides Hadley Wickham's purrr package for R, the fact that Apache Spark is written in Scala, and technologies related to MapReduce.
All of this sort of suggests to me that there should be some sort of relationship between category theory and Codd's relational algebra/calculus, but I have never heard of anyone making such a connection explicit or explain how it underlies the design decisions in popular data manipulation and relational database technologies. So I also suspect I could be entirely wrong.
EDIT: Apparently David Spivak has worked on a "functorial query language (FQL)". This sounds like it might be an application of such a theoretical connection, provided it exists.
Note: I am not sure if "relational-structures" is the appropriate tag for discussion of relational databases or relational algebra/calculus. This Wikipedia article suggests they might be connected, but ultimately I don't know what the phrase "relational structure" means. Please feel free to re-tag.