[elmolino89]

Probably way more important than lowering the CO2 is getting rid of PM2.5/PM10.

Rooftops nowadays are best used to mount solar panels. Some system growing circulating algae, be it on the roof or on the sun drenched walls while doable would have way higher at least the operating costs. Clining is one thing. If you live in the area with below zero temperatures either you drain the system or invest even more in some glasshouse, maybe thermal isolation at night or heating.

As mentioned by others, there are chemical solutions.

[elmolino89]

One can combine chemical absorber solution with electrolysis for the regeneration:

Efficient Direct Air Capture in Industrial Cooling Towers Mediated by Electrochemical CO2 Release

https://onlinelibrary.wiley.com/doi/10.1002/anie.202412697