Add /category/ to an author archive page

You can achieve this by adding a new rewrite rule using ‘add_rewrite_rule`.

If the category is the default WordPress category, you won’t have to register a query_var but if your category is a custom category, then you would have to register a query_var using the query_vars filter.

If category is the default WordPress category:

function wpse256215_custom_rewrite_rule() {
    add_rewrite_rule('^author/([^/]*)/([^/]*)/?','index.php?author_name=$matches[1]&category_name=$matches[2]','top');
}
add_action('init', 'wpse256215_custom_rewrite_rule', 10, 0);

If category is a custom query variable (author_category):

function wpse256215_custom_rewrite_rule() {
    add_rewrite_rule('^author/([^/]*)/([^/]*)/?','index.php?author_name=$matches[1]&author_category=$matches[2]','top');
}
add_action('init', 'wpse256215_custom_rewrite_rule', 10, 0);

function wpse256215_query_vars( $query_vars ) {
    $query_vars[] = 'author_category';
    return $query_vars;
}
add_filter( 'query_vars', 'wpse256215_query_vars' );

To use the custom query variable in your template, you can then use the get_query_var function:

$author_category = get_query_var( 'author_category' );

REFERENCE:

• add_rewrite_rule
• query_vars filter
• WP_Query
• get_query_var