First, put the following function in your functions.php file:
function get_cat_slug($cat_id) {
$cat_id = (int) $cat_id;
$category = &get_category($cat_id);
return $category->slug;
}
Once done, you can call the function as shown below:
<?php echo get_cat_slug(3); ?>
This will display the slug for the category with the ID 3.
Thanks to Ken Rosaka for the tip!
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WordPress trick: Get category slug using category ID