Definition:Free Category

Definition

Let $G$ be a digraph.

The free category on $G$, denoted $\map {\mathbf C} G$, is the category with:

Objects:		The vertices of $G$
Morphisms:		The walks in $G$
Composition:		concatenation of walks
Identity morphisms:		$\operatorname{id}_v$ is the empty walk at $v$

Also see

• Free Category is Category, which demonstrates that this is indeed a category.

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous): $\S 1.7$