Multi-layer views results
Yes, you can do this with a Contextual filter in Views. 

Create a Content View of your desired nodes, then add a Contextual Filter (I'm assuming your categories are actually Taxonomy terms referenced from nodes) for the Field with that Taxonomy reference. 

Configure it with these options:
    When the filter value is NOT available
    Display a summary
    Format List
    Base path (you must enter the Page path if this isn't the first Page Display in your Views)
    Display record count with link
    More
    Transform spaces to dashes in URL

This way you get a list of term IDs that link through to a list of nodes tagged with those terms. 

You probably want the term name to be displayed instead of the term ID. In that case remove the Contextual filter, we'll add the one for Taxonomy term Name, but we need a Relationship first for that information to become available. 

So add a Relationship Taxonomy term referenced from field_category (or whatever the field is called in your case), require it if you don't want summary results without a category. 

Then add a Contextual filter Name from Taxonomy term Category, it will use the Relationship we created, and configure it like above.