class Categorization < ApplicationRecord
  belongs_to :category
  belongs_to :provider
end

class Category < ApplicationRecord
  has_many :categorizations
  has_many :providers, through: :categorizations
  accepts_nested_attributes_for :categorizations
end

class Provider < ApplicationRecord
  has_many :categorizations
  has_many :categories, through: :categorizations
  accepts_nested_attributes_for :categorizations
end

<ul class="nav nav-justified nav-carousel upper-thumbs">
    <% Provider.order(created_at: :asc).take(6).each_with_index do |provider, index| %>
      <li id="<%= provider.name %>_<%= index + 1 %>" class="btn-up"><a data-href="#"><%= provider.name %></a></li>
    <% end %>
</ul>

<ul id="parent" class="nav nav-justified nav-carousel left-thumbs">
    <% Category.order(created_at: :asc).take(7).each_with_index do |category, index| %>
      <li id="aside_<%= index + 1 %>" class="btn-aside"><i class="category_image" style="background: url(<%= category.cat_image %>) no-repeat;"></i><a data-href="#"><%= category.name %></a></li>
    <% end %>
</ul>

var $btns = $('.btn-up').click(function () {
      if(this.id == 'a') {
          $('#parent > li#aside_1').fadeIn(450);
          $('#parent > li').not($('#parent > li#aside_1')).hide();
      } else {
          var $el = $('.' + this.id).fadeIn(450);
          $('#parent > li').not($el).hide();
      }
      $btns.removeClass('active');
      $(this).addClass('active');
  })