Civilization 5 BNW brings culture specific wonders. I'm wondering if those wonders maintain their effects after being captured if you haven't unlocked that social policy branch.
Civilization – Capturing Culture Specific Wonders
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Related Solutions
Although bwarner's answer was helpful as always, no one verified beyond "I think so" that puppet cities are affected by each of the civilization wide effects, so I did some testing and:
Yes, puppet cities are affected normally by all civilization-wide effects.
I can't verify that there are no exceptions, but I verified at least one of each of the things I was concerned about...
The Testing
Civilization Special Trait
I loaded up France on easy, and went about conquering. Japan fell, giving me Kyoto to play with. As soon as I conquered the city and took it as a puppet, it was producing 2 culture. This matches perfectly with France's ability, so CHECK!
More Test Setup
Having acquired my victim, I setup the test: social policy ready, golden-age ready, and wonder ready all on the same turn! (Save file available upon request, whenever I get around to it after that.)
Before
Social Policy
I enacted Liberty->Republic, which gives +1 production/city. That matches, so CHECK!
Golden Age
I already had culture working for me, so I started the golden age by enacting the social policy Piety->Reformation. Clearly shows an increase in both gold and production, CHECK!
World Wonder
If you take a look at all of my cities from the same turn, you can see Orleans is about to finish the Sistine Chapel, which gives +33% culture/city. I went to the next turn, and without any growth or buildings completing, the after shows increased culture on Kyoto. (Lyon also started with 7 culture and ended with 9 as well, so the rounding definitely matches.) CHECK!
Everything checks out. I suppose puppets really are just normal cities that you don't control. I would still love to hear if anyone finds any exceptions!
A lot of wonders (if not all of them?) show up as a visible model around the city in which they are constructing / constructed. So if you see a pyramid around a city, you know the the great pyramid is built there.
It takes some practice to know what wonder is what, and it's definitely a very crude way; requires scanning all cities for things that are sometimes very hard to notice. But it does work, I use this method often to know which wonder is being constructed by other civilizations, to avoid working on the same wonder.
Notice that all wonders have different "under construction" and "completed" models.
EDIT: I've found this wonderful page which attempts to catalog all wonders with screenshots of their "under construction" and "completed" models. Still incomplete, but useful nonetheless.
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Best Answer
Once a Wonder has been constructed by someone who has unlocked the right culture branch, its benefits are available to whoever owns that Wonder. If somebody builds Uffizi, and you capture the city that has it, then Uffizi - and all its benefits - are yours.