= Free category on independent arrows
{title2=$L(S)=\coprod_{s\in S}[1]$}
Take two distinct objects and one nonidentity arrow for each element of $S$, without arrows between different copies. A <functor> from this category to $\mathcal C$ is exactly a choice of one arbitrary arrow of $\mathcal C$ for each element of $S$. Consequently this construction is <left adjoint> to the functor taking the set of all arrows of a small category. Its free object has three arrows per generator, including the two identity arrows.
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