Rob's advice is very good in regard to sending people to the more effective inner page.
I would not mess around with canonical tags, unless the content is actually duplicated. Rethinking your internal links might be helpful. One thing I have done in similar situations is to use a keyword anchored link from the category page to the home page. Moz Analytics will tell you this is keyword cannibalization, but it does often work to nudge Google toward ranking the home page. So on a page about "Red Widgets", you could link to the home page with "Red Widget Company". What is likely to happen is that you will sort of split the searches based on user intent, and searches that are more than just the base keyword. Searches that Google thinks are more informational would go to the Red Widgets page, where someone looking for a supplier or maker of red widgets might be sent to the home page. Similar links throughout the site where they are appropriate would also be good. Like, if you have a page or a blog post that mentions red widgets, link to the category. If it says something about manufacturer of red widgets, link to the home page. Just like incoming links, you don't want to overuse the same keywords, though. Mix things up a bit within the same topical theme (red widget maker, manufacturer of red widgets, red widget company...)