Styjun

$.widget( "custom.catcomplete", $.ui.autocomplete, 
 _create: function() 
 this._super();
 this.widget().menu( "option", "items", "> :not(.ui-autocomplete-category)" );
 ,
 _renderMenu: function( ul, items ) 
 var that = this,
 currentCategory = "";
 $.each( items, function( index, item ) 
 var li, submenuUl;
 if ( item.category != currentCategory ) 
 var elt = $("<li class='ui-autocomplete-category'>" + item.category + "</li>");
 var submenu = $("<div class='submenu "+ item.category +"'><ul></ul></div>"); // Added <ul></ul>
 elt.append(submenu);
 ul.append(elt);
 currentCategory = item.category;
 
 submenuUl = ul.find("."+item.category+" ul"); // added +" ul"
 li = that._renderItemData(submenuUl, item );
 if ( item.category ) 
 li.attr( "aria-label", item.category + " : " + item.label ).addClass("ui-menu-item"); // Added the addClass()
 
 );
 
);


// Actual Code
$(function() 
 var data = [
 label: "annhhx10", category: "Products" ,
 label: "annk K12", category: "Products" ,
 label: "annttop C13", category: "Products" ,
 label: "anders andersson", category: "People" ,
 label: "andreas andersson", category: "People" ,
 label: "andreas johnson", category: "People" 
 ];

 $( "#search" ).catcomplete(
 delay: 0,
 source: data,
 select: function(item, ui) // Added item, ui --- Arguments were missing.
 console.log(ui.item.value);
 $( "#search" ).val( ui.item.value );
 return false;
 
 );	
);

#search 
 width: 500px;

.ui-autocomplete 
 display: flex;
 width: auto !important;


.ui-autocomplete-category 
 font-weight: bold;
 padding: .2em .4em;
 margin: .8em 0 .2em;
 line-height: 1.5;

.ui-autocomplete-category ul
 padding:0;

.submenu 
 font-weight: normal;


/* ADDED STYLE */
.ui-autocomplete>li>div>ul
 display: block !important;
 position: relative !important;
 border: 0 !important;

span.ui-menu-icon
 display:none !important;


/* ADDED for the SO snippet only !! Not needed on CodePen */
.ui-autocomplete>li
 display: inline-block !important;

<script src="//cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script src="//cdnjs.cloudflare.com/ajax/libs/jqueryui/1.11.2/jquery-ui.min.js"></script>
<link href="//code.jquery.com/ui/1.11.4/themes/smoothness/jquery-ui.css" rel="stylesheet"/>

<label for="search">Search: </label>
<input id="search">