I have the following graph
where $de = 1 = ce$, $dp = cq$, $dm = dq$, and $cm = cp$.
I would like to generate the free category from this graph. Its objects will be $0$, $1$, $2$. The definition says that its morphisms will be tuples of composable arrows. But I do not quite understand what it means.
Can $(e,d,e,c)$ be a morphism which I believe is a tuple of composable arrows?
Any help will be greatly appreciated.
Best Answer
What you have isn't a graph. $de=ce$ is an equation in a category, not in a graph. What we should do is first generate the free category and then apply your relations. That said, your proposed morphism indeed is one in the free category.