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                        at January 24, 2011 22:04 by lamebollock
                            
                            Initial Code
$('li.current_sub').prevAll("li.par_cat:first");
                                Initial URL
http://stackoverflow.com/questions/2310270/jquery-find-closest-previous-sibling-with-class
Initial Description
$('li.current_sub').prevAll("li.par_cat:first");
Tested it with your markup:
$('li.current_sub').prevAll("li.par_cat:first").text("woohoo");
will fill up the closest previous li.par_cat with "woohoo".
                                Initial Title
Find closest previous sibling with class
Initial Tags
jquery
Initial Language
jQuery