Adding, deleting elements as per autocomplete results
I know that this comes a few years late and the code doesn't appear to exist on the github repository anymore. Perhaps you have learned much more about jQuery and the autocompletes since posting this but none-the-less here is a review of it.

It is great that the DOM reference for the category input (i.e. $("#category_inp")) is stored in a variable but others could be also - like the container for the list of selected categories (i.e. $("#category_list")).

Instead of binding the enterKey event to a callback, why not use the select event callback option? That way if the user selects an option with the mouse the callback will also be called.

And for the delete image click handler, it could be simplified using .parent():

$(document).on('click', ".delete-cat", function (e) {
    $(this).parent().remove();
});