Applications for residence permits for family members will not be processed at the same time as the application of the main applicant during peak times (admission to the beginning of the autumn or spring semester). Often the co-applicant will therefore not be able to join the applicant in Sweden until a few months later.
For information on how to apply for a residence permit for co-applicants please follow the link and read the information provided by the Migration Agency.
Studying and researching in Sweden - Swedish Migration Agency (migrationsverket.se)