How to use category template elsewhere?

I love the category and author archive pages that are shown at /category/slug and author/slug . How can I use these layouts elsewhere? I want to use the same layout for an “all posts” page.

I’m looking at author.php and category.php (are those the right templates to look at?), but I’m confused about all these templates that seem to call each other, and I can’t figure out what’s needed if I create a new template to do this.