I am trying to learn some category theory and have noticed that sometimes parallel arrows appear in certain diagrams (for example: the definition of equalizer and coequalizer).
It seems to me that the usual intepretation of $X\overset{f}\rightarrow Y \overset{g}{\underset{h}\rightrightarrows} Z$ is $\begin{matrix} X&\overset{f}\rightarrow&Y\\ \;\;\downarrow_f&&\;\;\downarrow_g\\ Y&\overset{h}\rightarrow&Z \end{matrix}$
and the usual interpretation of the diagram $X\overset{g}{\underset{h}\rightrightarrows} Y \overset{f}\rightarrow Z$ is $\begin{matrix} X&\overset{g}\rightarrow&Y\\ \;\;\downarrow_h&&\;\;\downarrow_f\\ Y&\overset{f}\rightarrow&Z \end{matrix}$
At least with these two interpretations it seems that the definitions of equalizers and coequalizers can be phrased nicely in terms of commutative squares.
How do we interpret parallel arrows in general? For example, how does one interpret something like $X\overset{f}\rightarrow Y \overset{g}{\underset{h}\rightrightarrows} Z\overset{k}\rightarrow W$?
I guess what I'm looking for is a general interpretation of parallel arrows in terms of commutative squares, if that makes sense.