Add forward slash on categories url (serve one version of a url)

Filter category_link so WordPress creates slashed URLs for categories, and redirect_canonical so it accepts those URLs:

add_filter( 'category_link', 'wpse_71666_trailingslash_cat_url' );
add_filter( 'redirect_canonical', 'wpse_71666_trailingslash_cat_url', 20, 2 );

function wpse_71666_trailingslash_cat_url( $url, $request="" )
{
    if ( 'category_link' === current_filter() )
        return rtrim( $url, "https://wordpress.stackexchange.com/" ) . "https://wordpress.stackexchange.com/";

    if ( "$url/" === $request and is_category() )
        return $request;

    return $url;
}