In theory yes, but the routing implementation of Laravel 4/5 is buggy and optional parameters cause routes to fail:
You can only try to work around this by creating a separate page and route that are used when a category is shown and the "f_name" and "f_catid" parameter are mandatory.
Help for integrating the Laravel package
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Yvler wrote:That was our backup plan and we'd probably create another table where a slug is saved and where this slug is linked to these parameters
You don't need another table. The mshop_catalog and thus the catalog items contains all you need, including the possibility to define URL segments (a.k.a. slugs) as associated texts.