Changing the sidebar of Blog categories overview pages

Hello again

Is there a way of changing the sidebar in certain categories of blog posts overview ‘pages’ to a non default one? At the moment, my blog page and individual blogs have my “updates” sidebar, but when you click on one of the category tags to find similar content, the sidebar on that overview page reverts to the site’s default sidebar.

If I need to change the default sidebar, I can do that, but I wondered if there’s another way.

With thanks! Ruth