I've set up a very light jquery tab system for a website:

starting from this HTML code: 


<ul class="pates-tabs__list">
  <li class="pates-tabs__item">
    <a href="#presentation" id="label_presentation" class="pates-tabs__link">Présentation</a>
  </li>
  <li class="pates-tabs__item">
    <a href="#ingredients" id="label_ingredients" class="pates-tabs__link">Ingrédients</a>
  </li>
  <li class="pates-tabs__item">
   <a href="#preparation" id="label_preparation" class="pates-tabs__link">Préparation</a>
  </li>
  <li class="pates-tabs__item">
   <a href="#conditionnement" id="label_conditionnement" class="pates-tabs__link">Conditionnement</a>
  </li>
</ul>

<div id="presentation" class="pates-tabs__tabcontent"> 
 1
</div>
<div id="ingredients" class="pates-tabs__tabcontent"> 
 2
</div>
<div id="preparation" class="pates-tabs__tabcontent"> 
 3
</div>
<div id="conditionnement" class="pates-tabs__tabcontent"> 
 4
</div>



Styles CSS are based on ARIA attributes :


[aria-hidden=true] {
  display: none;
}



and jQuery code will do the rest:


  /* loading aria attribute on pates tabs */
  $('.pates-tabs__list').attr('role', 'tablist');      // ul
  $('.pates-tabs__item').attr('role', 'presentation'); // li
  
  $('.pates-tabs__link').attr('role', 'tab');          // a
  $('.pates-tabs__link').each(function() {             // controls attribute
     $this = $(this);
     controls = '' + $this.attr('href');
     controls = controls.replace('#','');
     $this.attr('aria-controls', controls);
     $this.attr('tabindex', '-1');
  });
  
  $('.pates-tabs__tabcontent').attr('role', 'tabpanel');    // contents
  $('.pates-tabs__tabcontent').attr('aria-hidden', 'true'); // all hidden
  $('.pates-tabs__tabcontent').each(function() {            // label by link
     $this = $(this);
     labelledby = 'label_' + $this.attr('id');
     $this.attr('aria-labelledby', labelledby);
  });
  
  // hash => select the good one
  hash = window.location.hash;
  hash = hash.replace('#','');
  $('.pates-tabs__tabcontent').each(function() {
     $this = $(this);
     if ( hash == $this.attr('id') ){
         selector = '#' + hash;
         // affichage
         $(selector).removeAttr('aria-hidden');
         // selection menu
         selector = '#label_' + hash;
         $(selector).attr('aria-selected', 'true');
         $(selector).attr('tabindex', '0');
         return false; // on sort du each
     }
  });
  // if no selected => select first
  if ($('.pates-tabs__link[aria-selected]').length == 0) {
     $('.pates-tabs__link:first').attr('aria-selected', 'true');
     $('.pates-tabs__link:first').attr('tabindex', '0');
     $('.pates-tabs__tabcontent:first').removeAttr('aria-hidden');
  }
  
   
  /* click on a link */
  $('.pates-tabs__link').click(
     function() {
      $this = $(this);
      
      // remove aria selected on all links + remove focusable
      $('.pates-tabs__link').removeAttr('aria-selected');
      $('.pates-tabs__link').attr('tabindex', '-1');
      
      // add aria selected on $this + focusable
      $this.attr('aria-selected', 'true');
      $this.attr('tabindex', '0');
      
      // add aria-hidden on all tabs
      $('.pates-tabs__tabcontent').attr('aria-hidden', 'true');
      
      // remove aria-hidden on tab linked
      id_to_show = '#' + $this.attr('aria-controls');
      $(id_to_show).removeAttr('aria-hidden');
      
      return false;
      }
    );

  $('body').on('keydown','.pates-tabs', function(event) {
  
      // strike up or left in the tab
      if (event.keyCode == 37 || event.keyCode == 38) {
         // find previous tab
         // if we are on first => activate last
         $activated = $('.pates-tabs__link[aria-selected="true"]').parent();
         if($activated.is('.pates-tabs__item:first-child')) {
            $('.pates-tabs__item:last-child a').click().focus();
            }
            else { // else activate previous
                 $activated.prev().children('.pates-tabs__link').click().focus();
                 }
         event.preventDefault();
         }
      // strike down or right in the tab
      if (event.keyCode == 40 || event.keyCode == 39) {
         // find next tab
         // if we are on last => activate first
         $activated = $('.pates-tabs__link[aria-selected="true"]').parent();
         if($activated.is('.pates-tabs__item:last-child')) {
            $('.pates-tabs__item:first-child a').click().focus();
            }
            else { // else activate next
                 $activated.next().children('.pates-tabs__link').click().focus();
                 }
         event.preventDefault();
         }

      //event.stopPropagation();
      //return false;
      
      }
    );
  /*********************************************************************************************************/
  


There it is.