Having Category appear on Sub-domain

I have a question that might be a bit tricky to accomplish.

Basically, I have a website that is fully WordPress-powered with a custom skin. This website generally supplies “lessons” (instead of traditional blog posts). However, now I want to add a “blog” to my website, that functions as a blog.

Right now I have all of those categories parented to a Blog category (with a slug of blog). So, all of the URLs are like https://www.mydomain.com/blog/category1/my-post.

What I’d like to do now is to do is make it so it’d appear like: blog.mydomain.com/category1/my-post.

Does anyone know of a setting, hack, or plugin that would let me accomplish this? (Of course, I can add the subdomain itself, I just need the means to redirect it).

Thanks.