Category Image inside the loop

Hello guys!

I have a page, that displays posts from some categories. I need to show a picture, instead of category name.

So.. I think, I heed something like this:

Category: <img src="http://mywebsite.com/images/<?php the_category_id(); ?>.png">

I was trying to find such function, but with no success 🙁

Could anyone help me with that??
Thank you!