In the first post of this series, we saw how graphs and symmetric graphs are -sets and how they are implemented in Catlab.jl. Such graphs mildly generalize the concept of graph familiar from combinatorics and computer science. They are preferred by category theorists because every small category has an underlying graph in this sense,1 and so categories can be seen as graphs with composable edges. There is, however, another notion of graph, based on “half-edges” or “darts,” that is popular in parts of physics (Marcolli and Port 2015; Markl, Merkulov, and Shadrin 2009), topological graph theory (Lando and Zvonkin 2004), and computational geometry.
This is a companion discussion topic for the original entry at https://blog.algebraicjulia.org/post/2020/09/cset-graphs-2/index.html