Index page when entered to the category link

Hi.
I know that the title is not really “descriptive”, but I did my best to make it a “brief” one.

The thing I want to do is, make an index page out of the category links. Let me tell you this way. I have a site, which has movie reviews and stuff like that. It has a category called “Trailers”, and subcategories from A-to-Z. When I enter myadress.com/cat/trailers, I don’t want to see the posts on that category, I want to see links to the subcategories like “A – B – C – D – E … X – Y – Z”. Is that possible? And how can I do that, some advice would be nice. Even if you could tell me where to start, I think I can manage to find how to do it. But right now, I don’t have a clue…

Thanks in advence…