Show Excerpts Only on Category Pages

I’d like to use my WordPress blog as a Photo album, like this:

Each photo gets its own post, assigned to one or more categories. The main content of the post is the photo itself, while the excerpt contains a thumbnail linked to the main post.

When viewing each post individually, you only see the main content, not the excerpt.

When a user clicks on a category, I want them to see a list of all posts assigned to that category, listed ONLY by their excerpt. (so that when they click on the thumbnail, it takes them back to the individual post, where they only see the main content — the large photo.)

I hope this make sense. Can anyone offer a suggestion?