Is a Shul required to build a Sukkah?
It is customary for a Shul to have a Sukkah built near the premises of the Shul for the sake of guests to eat in it during Sukkos. [However, individuals who live in the city are not to rely on the Shul’s Sukkah, if they have the premises available to build one near their home.]
 Teshuvos Hageonim Tractate Sukkah 51-53 “Regarding that which you asked if today one is obligated to build a Sukkah in synagogues and Batei Medrash or not? The answer is as follows: We know that the Jewish people are only obligated to build a Sukkah near their home where they can eat and drink just as they do in their home, while a synagogue is only designated for prayer. Nonetheless if they build a Sukkah for the sake of the passersby and guests this is a very good thing.”; Likkutei Sichos 19 p. 289
 See Teshuvah Hageonim ibid “However, the people of the city are not to rely on the Shul’s Sukkah to fulfill their obligation, as one only fulfills his obligation with a Sukkah that he makes near his home.”