Only show excerpts on "Categories" page for Twenty Fifteen Theme

As the title says, I’m trying to figure out how to get the site to only post excerpts of my posts when I click a certain category. I’d prefer to not use another plugin. I also only want the excerpts to be for the categories page. The main page will continue to display the entire post.

I know I’ll probably need the_excerpt() function (or something similar?). I’m also unsure of which .php file I would need to be editing.

But if someone can help point me to the right direction, I’d be very grateful!