JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://getbootstrap.com/dist/css/bootstrap.min.css">
<script src="http://getbootstrap.com/dist/js/bootstrap.min.js"></script>
<ul class="nav navbar-nav">
  <li class="dropdown mega-dropdown">
    <a href="javascript:;" class="dropdown-toggle" data-toggle="dropdown">
      <i class="fa fa-"></i> Menu item 1
      <span class="fa fa-chevron-down pull-right"></span>
    </a>
    <ul class="dropdown-menu mega-dropdown-menu">
      <li>
        <div id="carousel" class="carousel slide" data-ride="carousel">
          <ol class="carousel-indicators">
            <li class="" data-slide-to="0" data-target="#carousel"></li>
            <li class="active" data-slide-to="1" data-target="#carousel"></li>
          </ol>
          <div class="carousel-inner">
            <div class="item">
                <img alt="" class="img-rounded" src="//placehold.it/360x240/&text=Hello" />
            </div>
            <div class="item active">
                <img alt="" class="img-rounded" src="//placehold.it/360x240/&text=World" />
            </div>
          </div>
          <a data-slide="prev" role="button" href="#carousel" 
             class="left carousel-control">
            <span class="glyphicon glyphicon-chevron-left"></span>
          </a>
          <a data-slide="next" role="button" href="#carousel" 
             class="right carousel-control">
            <span class="glyphicon glyphicon-chevron-right"></span>
          </a>
        </div>
      </li>
    </ul>
  </li>
</ul>

JavaScript

$('ul.dropdown-menu.mega-dropdown-menu').on('click', function(event) {
    event.stopPropagation();
});

$('a.left').click(function () {
    $('#carousel').carousel('prev');
});

$('a.right').click(function () {
    $('#carousel').carousel('next');
});

$('ol.carousel-indicators li').click(function (event) {
    var index = $(this).data("slide-to");
    $('#carousel').carousel(index);
});