get category ID in function.php

Hi, I’m modifying my function.php theme file to show posts that match these criterias:
1) posts of the user logged in
2) posts of the same category of the post shown
I managed to match the first criteria, but not the second one.
This is the code of the function:

<?php
function get_related_author_posts() {
    global $authordata, $post, $current_user;
    get_currentuserinfo();
    $authors_posts = get_posts( array( 'author' => $current_user->ID, 'post__not_in' => array( $post->ID ), 'posts_per_page' => 10, 'category' => ?????? ) );
    $output = '<ul>';
    foreach ( $authors_posts as $authors_post ) {
        $output .= '<li><a href="' . get_permalink( $authors_post->ID ) . '">' . apply_filters( 'the_title', $authors_post->post_title, $authors_post->ID ) . '</a></li>';
    }
    $output .= '</ul>';
    return $output;
}
?>

I should pass the ID of the category, into the get_posts parameters, but I don’t know how to get the category ID of the post that the user is viewing.

So, simplyfing, what I substitute the question marks with?
$authors_posts = get_posts( array( 'author' => $current_user->ID, 'post__not_in' => array( $post->ID ), 'posts_per_page' => 10, 'category' => ?????? ) );

Thank you very much! ??

Rocco