User groups in relation to categories
I believe your problem lies in the parameter for user group. In Twig, you don't need the brackets if you're already in brackets. You just reference the variable and fields directly. So instead of:

{% set group = craft.users.group('{{ category.slug }}') %}


Try this:

{% set group = craft.users.group(category.slug) %}


You see, the ElementCriteriaModel that's parsing the parameter for group doesn't run all its function arguments through Twig. So you're confusing it by throwing braces in there. Just give it the variable and field without quotes or braces and it should work smashingly, provided that category.slug is the same as a group slug.