infer post type when query var is not set

functions.php

<?php

function berkeley_find_post_type() {
	
	$type = get_query_var( 'post_type' );
	
	if ( ( !isset( $type ) || empty( $type ) ) && is_tax() ) {
		// we're on a term archive, where post type might not be set but can be inferred from taxonomy's object_type
		$current_term = get_queried_object();
		$tax_obj = get_taxonomy( $current_term->taxonomy );
		if ( count( $tax_obj->object_type ) == 1 )
			$type = $tax_obj->object_type[0];
	}
	
	return $type;
}