Whether you need a visa to stay in Sweden depends on which country you are a citizen of. The requirements for obtaining a visa are the same regardless of whether you are taking part in a cultural exchange, residency or conference.
Citizens from EU, EEA and Schengen countries
If you are a citizen from the EU, EEA or Schengen countries, you do not need a visa to visit Sweden. There is free movement between countries in the EU, EEA and Schengen.
Citizens from outside EU, EEA and Schengen countries
If you are visiting Sweden for up to 90 days during a six-month period, you may need to apply for a visa.
If you are visiting Sweden for more than 90 days, you must apply for a residence permit.
Some special requirements for visas can apply
The Swedish embassy or consulate-general in the country you are coming from has more information on the rules that apply. Keep in mind that conditions can vary from country to country.