I wish to ask a question about category theory applied to programming, what would be the best place?
In the TSC.SE help center, it says that they "welcome research-level questions in theoretical computer science", so if your question "can be discussed between two professors or between two graduate students working on Ph.D.'s" then you can probably ask it there.
In the CS.SE help center, it says that computer science is "is the science of computation and its applications", so your question could probably be asked here too, if you don't think it fits the requirements of TCS.SE.
There is also a chance that your question would be on-topic at Programmers.SE. I can't really tell how your question would fit the guidelines set on the Programmers.SE help center, so you would have to be the judge of that.
Personally, I think your best bet would be to ask on Computer Science.SE. So, go ahead, ask away!