how to theme content type based on context
Here is a complete solution


Installing context module we can create a context which comprise of conditions which if they are met they do the specified reactions
Installing entity_field_condition will let as set the desired condition
Add context (lets name alternative theme section)
Add Node Field (entity_field_condition) and select category name and choose the specific value that corresponds to the desired category (tid since we are talking about term reference).
Add reaction theme and choose the theme that you want to be activated on above conditions


NOTES:
At the time of writing this entity_field_condition needs a patch to work properly with entity reference (as is the case of category field).  The patch can be found here 

term condition was not working at the moment (buggy was not able to add the condition it was giving WSOD)

Alternatives would be to write my own custom condition or debug the term condition module or write my own theme negotiator