In view of the relation between categories with their underlying (reflexive) directed graphs and in view of the notion of *dagger-categories* it makes sense to say that:

A *$\dagger$-graph* is a (reflexive) directed graph equipped for each pair of vertices $x,y$ with an involution $\sigma_{x,y} \colon V(x,y) \to V(y,x)$ on sets of edges between these vertices, changing the direction.

This is one way to think of *undirected* graphs as directed graphs with extra structure. In fact, some authors define pseudographs to be directed graphs equipped with such an involution.

The point of the terminology here is that the underlying graph of any dagger-category is canonically a dagger-graph, in the above sense.

Last revised on June 5, 2023 at 06:17:37. See the history of this page for a list of all contributions to it.