Magento 2 – How to Redirect from PHTML File

Get the category from the Magento product. Override the controller in a module and before the redirect use:

$ids = $product->getCategoryIds();
$_category = Mage::getModel('catalog/category')->load($ids->getFirstItem());
$redirect = $_category->getUrl($_category); 
$this->getResponse()->setRedirect($redirect);

and use $redirect to make it happen. This code is untested, but the approach should work.

What I would do is returning the url to redirect in a JSON object (for example) as response to Ajax call, and then deal with that response in the .phtml

So...

public function execute()
{
    $response = new stdClass();
    $response->url = false;
    // your logic here, where you set the redirect url in $response->url if proceed
    die(json_encode($response));
}

And then, in .phtml

$("#addToCart").click(function(){ 
    var controllerUrl = "<?php echo $block->getUrl('batchorder/index/addtocart'); ?>";
    $.post( controllerUrl, function( response ) {
        if (response.url){
            window.location.href = response.url;
        } else {
            // show some error
        }
    });
});