How to control template resolution if both Author and Category filter in place?

You could change the template loaded by hooking onto template_include, checking if is_author and is_category are both set, then switch the template for inclusion to the author template instead.

Give this a shot..

add_filter( 'template_include', 'my_template_setter' );
function my_template_setter( $template ) {
    if( is_author() && is_category() && is_archive() )
        $template = get_author_template();
    return $template;
}

You can do any number of conditional checks here before modifying which template gets loaded.

WordPress has several template fetching functions available already, i’ve used one in the example, but here’s a list for quick reference…

get_404_template()
get_search_template()
get_taxonomy_template()
get_front_page_template()
get_home_template()
get_attachment_template()
get_single_template()
get_page_template()
get_category_template()
get_tag_template()
get_author_template()
get_date_template()
get_archive_template() 

Hope that helps..