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

I suggest you to read the docs about relations. 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