This is a default part of the custom taxonomy functionality built into WordPress. When you register your taxonomy, the following argument play a part in determining whether to display that archive and where:
public(is it accessible on the front end?)rewrite(how do the permalinks work?)
You should read through all of the arguments closely to understand how they work.
You also need to make sure that your taxonomy name does not collide with any of the reserved terms.
Finally, there’s already a ‘Category’ taxonomy, so you may be better off just adding that taxonomy (that is already on Posts) to your custom post type. You would do that in your register_post_type() function with the taxonomies argument like it’s done here.