Remove default sidebar?

I want a site with now side bars so I chose the full width settings for my site and pages. However, when someone is viewing a post it gives a link to the category. When I click on the category I see a blog of the category (this is fine) but the default sidebar shows up on the bottom right (Random Posts, Search by Tags etc.) How do I
a) get rid of this sidebar
OR
b) make the category link go away?

Thank you!