# nLab enriched directed loop graph

Contents

### Context

#### Graph theory

graph theory

graph

category of simple graphs

# Contents

## Idea

A directed loop graph may be understood as a thin (0,1)-directed pseudograph, hence as a thin directed pseudograph enriched over the cartesian monoidal poset of truth values. In generalization, one may speak of enriching directed loop graphs over other monoidal posets.

## Defintion

Let $(M, \leq, \wedge, \top)$ be a monoidal poset, such as a meet-semilattice. A $M$-enriched directed loop graph or directed loop graph enriched over/in $M$ is a set $P$ with a binary function $o:P \times P \to M$