When you say "competing", do you mean the category page and homepage are close together in the SERPs or just optimized for the same keyword? Did you intentionally optimize the homepage for that keyword?
It all comes down to which page is truly more relevant to the search query. For example, let's pretend you and your competitor sell dog accessories (collars, leashes, food, toys, etc). Someone searching for "dog leashes" would much rather land on your page for "dog leashes" rather than your homepage or your competitor's homepage since it puts them on exactly what they were looking for (rather than having to navigate their way from your homepage to the dog leashes page). Make sense?
Also, assuming your category page is intended to outrank your homepage for that keyword, you wouldn't be competing with your homepage unless it is ranking higher than your category page. Having your homepage ranking for that same keyword is only an issue if it appears before your category page in the SERPs.
Hope that helps!