The trouble with C-sets is that they cannot model data structures such as labelled graphs, which are graphs where every edge and vertex has an associated element from some set of labels. In this blog post, we will discuss an extension to C-sets which we call attributed C-sets that solves this issues. This formalism is mainly inspired by the viewpoint of the “Algebraic Databases” paper (Schultz et al. 2016), though in truth we take more after the “databases” part than we do the “algebraic” part.
This is a companion discussion topic for the original entry at https://blog.algebraicjulia.org/post/2020/10/acset-theory/index.html