For improvement adjacency, do I need to specify unique districts?

[Brixter]

Do I need to specify the unique districts for the improvement adjacency? For example, Batey has adjacency bonus to Entertainment Complex. Do I need to specify the unique versions of the district (Street Carnival and Hippodrome)?

Mahavihara specifies Lavra and Observatory explicitly but the other improvements specify only the normal district. Do the other improvements don't work with the unique districts?

 

[Brixter]

Apparently, except for Mahavihara, all improvements only work with the regular versions of the district.