Is there any obligation to supervise the private renovation of the air duct property in the downstairs store?

The property has the responsibility of supervision, but it is wrong for you not to pay the property fee.

According to Article 46 of the Property Management Regulations

The realty service enterprise shall stop the violation of laws and regulations such as public security, environmental protection, property decoration and use in the realty management area, and report to the relevant administrative departments in a timely manner.

Article 50

Public buildings and facilities planned and constructed within the property management area shall not be changed.

If the owners need to change the use of public buildings and facilities according to law, they shall inform the property service enterprises after handling the relevant formalities according to law; If the realty service enterprise really needs to change the use of public buildings and facilities, it shall be submitted to the owners' meeting for discussion and approval, and the owners shall go through the relevant formalities according to law.

Visible property services companies should stop, and report to the relevant departments. If not, they have failed in their duties. You can also check the property service contract you signed to see if there are any breach clauses, and then find evidence to sue the property company.

However, it is not appropriate for you to resist in the form of payment. In the future, if they want to sue you, you should lose. The only way to correct property breach is to ask for correction. If you don't correct it, you can complain or sue to the Housing Authority.