Dimensions with special roles may have special properties in JSON-stat. For instance, dimensions with the "geo" role support "coordinates"
and dimensions with "metric" role support "unit"
But that's about it. For any property not supported in the spec, you need to use "extension".
Take into account that "extension" can be attached at three different levels. Because in your case you need new properties to describe categories the right level is the dimension one. See for example *.dimension.concept.extension.definition.UNR in
X.