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My solution to this is to add a 'T' connector on the back of the capture card so the feed is split. One branch goes to your PC, the other to a TV. Total cost about 50p!
There are a couple ways that this might be possible. Some capture cards are also capable of producing a composit output but are not supported very well by the linux kernel.
The second way to do this would be a video card that has a composit out or a converter.