Why do we sometimes write reactants above the reaction arrow?

We write:

$\ce{Alcohol ->[\ce{KMnO4}] Acid}$

The alcohol forms a carboxylic acid, i.e. gains an $\ce{O}$ from $\ce{KMnO4}$. This means $\ce{KMnO4}$ is a reactant! Then why is it written above the arrow?

What else do we write above the arrow?

• If we only care about what happens to alcohol it's useful notation. – Mithoron Mar 17 '15 at 14:33
• Btw, if you're interested in using $\LaTeX$ for math and equations and really want really sharp looking chemical equations, have a look at all the options provided by the mhchem package. Check out this and the original documentation at CTAN. You will love it! – Klaus-Dieter Warzecha Mar 17 '15 at 14:56

Things written on arrows are chemicals that are part of the reaction in some way, but not one of the reactants or products. In this case, the $\ce{KMnO4}$ is your oxidizing agent, which can be swapped out for any other strong oxidizer, and is not an inherent part of the reaction.
Other things you could see on the arrow would be $\ce{H2O}$ or Diethyl Ether, both of which are solvents. Other things include $h\nu$ and $\Delta T$, both of which are conditions under which the reaction takes place. Lastly the most common thing you'll see are catalysts such as $\ce{Pt}$. As you can see, all of these things are necessary to the reaction, but aren't really what we care about in the reaction/can be substituted for other, similar chemicals.