Index.php loaded instead of category.php

Am new to building WP themes, so just to double check a basic question: category.php should be loaded simply by the URL being, say, example.com/category/shows right?

My WP installation for some reason is loading index.php instead of category.php. I have also tried creating a specific category file, category-3.php (I understand the only way to get this is from the Categories admin screen by looking at the tag_ID in the URL?), but this doesn’t get loaded either.

I’ve done various printouts to verify that this is what’s going on, but am slightly mystified as to the reason.

I’m building a custom theme for my site but I switched temporarily back to the Twentytwelve default theme and it seems to have the same problem.

It’s a fresh install on a newly setup host and I haven’t touched any ht access files.

Thanks!

(PS I found similar topics on this forum but none seemed to address this specific issue. Apologies if I missed something.)