An Alliance uniform cap, maybe
November 6th, 2009 | 
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New, at the Prop Store of London: an Alliance uniform cap. But the description puzzles me:
A purple cap with a triangular patch on the front made for the sci-fi action film Serenity. The cap is similar to the version worn by the Alliance soldiers onboard the Operatives ship when it is attacked by the Reavers. One size fits most.
"Similar to"? Is it an actual costume prop or a replica? The price ($59) suggests it's a real costume prop — too pricey for a home-made or licensed replica, I would think — but maybe one that never saw screen time, which would cost much more. And it's listed under Props, instead of Replicas. The Prop Store is usually better about such distinctions. Maybe they couldn't conclusively identify where it was used, so declined to say either way?
Whichever it is, it's a nice looking cap for your purple-belly friends.
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The thing is, I clearly see a Caduceus, which is a pretty universal symbol for medicine.
Without checking, I'd say it's far more likely this is the cap worn by Mal or Zoe in "Ariel" when they were posing as paramedics.
I'm pretty sure the cap was definitely made for the movie and is not a replica. My take on this is that the hat was made for production, but probably not used in the film or didn't appear on screen. They say it is similar to the alliance hat's on the operative's ship because those were the same purple baseball caps but with a silver alliance logo badge on them. Make sense?