To determine whether a specific product category exists in the WooCommerce cart, use the woocommerce_before_cart_contents hook. This allows you to run a function just before cart items are rendered. Here's how you can set it up:

add_action('woocommerce_before_cart_contents', 'check_product_category_in_cart');

function check_product_category_in_cart() {
    $category_slug = 'your-category-slug'; // Enter the category slug you're targeting
    $category_found = false;

    $cart_items = WC()->cart->get_cart();

    foreach ($cart_items as $key => $item) {
        $product_id = $item['product_id'];

        if (has_term($category_slug, 'product_cat', $product_id)) {
            $category_found = true;
            break;
        }
    }

    if ($category_found) {
        echo 'The category is in the cart.';
    } else {
        echo 'The category is not in the cart.';
    }
}

Replace 'your-category-slug' with your actual category slug. You can insert this snippet into your active theme’s functions.php file or your custom plugin. It checks the cart contents and prints a message depending on whether the target category is present.