It's possible in the item view. Just enable Facebook or any other supported social widget through the relevant category "display settings".

If you want to add a like button in a category listing, you'll have to override the category_item.php file in K2. For more on overriding K2 template files: getk2.org/documentation/tutorials/templating-with-k2-and-the-concepts-of-sub-templates

It's a matter of appending the necessary Facebook widget code wherever you want the button to display.