file.php

<?php
/*
 * Get category from query_var of current page
 *
 * http://codex.wordpress.org/Function_Reference/get_query_var
 * http://codex.wordpress.org/Function_Reference/get_term
 * http://codex.wordpress.org/Function_Reference/get_term_by
 * http://codex.wordpress.org/Function_Reference/get_category_by_path
 * http://codex.wordpress.org/Function_Reference/get_category_by_slug
 * http://codex.wordpress.org/Function_Reference/get_the_category
 * http://codex.wordpress.org/Function_Reference/get_category
 */

     $category = get_query_var( 'category_name' );

     $category = get_term_by( 'slug', $category, 'category' );

$category_name = $category->name;

$category_slug = $category->slug; // OR // get_query_var( 'category_name' );

$category_desc = $category->description;

?>