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Options

$$ \large\begin{matrix} A & \overset{f}{\longrightarrow} & B \\ g \downarrow & & \downarrow h \\ C & \overset{i}{\longrightarrow} & D \end{matrix} $$ 1) Write down the ten paths in the free square category above.

2) Name two different paths that are parallel.

3) Name two different paths that are not parallel.

## Comments

\(\mathrm{id}_A,\mathrm{id}_B,\mathrm{id}_C,\mathrm{id}_D,f,h,g,i,h\circ f,i\circ g\)

Among these, only two paths are parallel (i.e., have the same source and target objects): \(h\circ f\) and \(i\circ g\).

Any two other paths are not parallel, for example, \(f\) and \(g\).

`\\(\mathrm{id}_A,\mathrm{id}_B,\mathrm{id}_C,\mathrm{id}_D,f,h,g,i,h\circ f,i\circ g\\) Among these, only two paths are parallel (i.e., have the same source and target objects): \\(h\circ f\\) and \\(i\circ g\\). Any two other paths are not parallel, for example, \\(f\\) and \\(g\\).`