class DuplicateCategory extends MagentoBackendAppAction {
protected $_categoryFactory;
public function __construct(
MagentoBackendAppActionContext $context,
MagentoCatalogModelCategoryFactory $categoryFactory
) {
parent::__construct($context);
$this->_categoryFactory = $categoryFactory;
}

$parentCategoryObj = $this->_categoryFactory->create()->load(2);
$duplicateCategoryObj = $this->_categoryFactory->create()->load(8);
$catagoryObject = $this->_categoryFactory->create();

$categoryName = $duplicateCategoryObj->getName();
$categoryUrlKey = strtolower($this->getCategoryUrlKey($categoryName));

$catagoryObject->setPath($parentCategoryObj->getPath())
->setParentId($parentCategory)
->setName($duplicateCategoryObj->getName())
->setUrlKey($categoryUrlKey)
->setStoreId($storeId)
->setIsActive(true);
$catagoryObject->save();
}