If we let $U$ be a class and let disjont sets $Q(A,B)$ be given for each pair $(A,B)\in U^2$ then the associated path category is the category $\mathfrak{C}$ with:
$ob(\mathfrak{C})=U$ and morphisms given by sequences $(f_1,..f_n)$ where we have that $target(f_i)=source(f_{i+1})$ and composition is given by concatenation.
I want to show that the categroy $Sets$ is not a path category but I am not really sure how to proceed with this? Any help would be appreciated
Hint: does a path category have (co)products?