They’re very powerful ajax libraries but…what happens when you use them together? There are some conflicts because they all override $ function.
So if you want to use different libraries that are using both JQuery, Prototype and Mootools, like Lightbox, Slimbox, Thickbox, JSValidate or something else, you can use noConflict function. It’s only a JQuery feature, so you can use JQuery with Prototype or JQuery with Mootools. I never tried Prototype with Mootools but it seems there isn’t still a similar function like noConflict in these libraries.
This is the code you can set for calling JQuery:

<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript">var $JQ = $; //rename $ function</script>

and then you must use the new prefix, $JQ, insted of $ for every JQuery call. For example, if you’re using Thickbox just replace every instance of $ with $JQ inside thickbox.js

Sources:
JQuery
Davide Salerno
Filippo Pisano