[asavinov]

> I always felt like there was some super deep & fundamental link between these mathematical concepts and relational modeling ideas.

The relational model is relies on set theory (more specifically relational algebra). An alternative view on data and data modeling is based on 1) sets, and 2) functions, and is called the concept-oriented model [1, 2]. It is actually quite similar to category theory and maybe even could be described in terms of category theory. It is also quite useful for data processing and there is one possible implementation which is an alternative to map-reduce and join-groupby approaches [3].

[1] A. Savinov, On the importance of functions in data modeling https://www.researchgate.net/publication/348079767_On_the_im...

[2] A. Savinov, Concept-oriented model: Modeling and processing data using functions https://www.researchgate.net/publication/337336089_Concept-o...

[3] https://github.com/asavinov/prosto Prosto is a data processing toolkit radically changing how data is processed by heavily relying on functions and operations with functions - an alternative to map-reduce and join-groupby