I suggest you to read the docs about [relations][1]. You can search for relations by the following parameter
In its simplest form, you can pass in one of these things to it:
An AssetFileModel, CategoryModel, EntryModel, UserModel, or TagModel object
An element’s ID
An array of element objects and/or IDs
What you pass is a string or to be more specific a url
<option value="{{category.url}}">{{ category.title }}</option>
What you have to do is:
<option value="{{category.id}}">{{ category.title }}</option>
In order to find users related to a category id.
However I strongly suggest you to build your search with PHP if you are going to include multiple parameters (more categories/search terms/complex and+or bindings) it is going to be a mess with twig [1]: https://craftcms.com/docs/relations#the-relatedTo-param