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$\newcommand{\Hom}{\operatorname{Hom}}$Suppose we want to define the category of arrows of $S$. Below are two forms of doing it.
Definition 1: If $D$ is of the following type: $\bullet \to \bullet$, then the category $\Diag(D, S)$ is called the category of arrows of $S$, denoted $\Fl(S)$.
Defi...