Slideshow from Category Page Post Thumbnails

I am building a website in a child theme of twentytwelve. What I am trying to do is create a slideshow within the main sidebar. This area will be about 250×106 and will appear above other widgets within the widget area.

My question: is it possible to create a slideshow that will pull the image from each post in a category page template? So, if I have a page template called “Our Sponsors” that displays posts with the category of “sponsors”, can I have those posts feed into this slideshow contained within the main sidebar? If a photo is not attached to that post, the slideshow will display the title of that post.