In reply to Wayne Goldring:
You'll get a little bit of sag regardless, because zero sag means infinite tension in the rope. If you were able to buy a magically weightless and stretchless infititely strong rope, you'd just move the trees (or break your rigging) instead.
With a 4kg camera and 100m span, and with the rope sagging very little, the tension in the rope is more or less 200kg/(how far it's sagging).
So, 1m sag -> about 200kg worth of tension, 10cm sag -> about 2 tonnes.
(That's assuming you have that magic weightless rope, which obviously you won't have - so in the real world it'll be more severe even than that.)
The bottom line is that regardless of the rope, it's probably not going to be practical to rig the rope over such a long span at head height and eliminate the sag in the middle.
If you can raise the rope up a bit to deal with say about 1.5 - 2m sag you might well be able to use an abseiling rope. They are manufactured to be slightly stretchy though, to give them shock-absorbing qualities they need to cope (and help the rigging to cope) with minor falls, jerks and shock loads that are common the way they're used in climbing and caving.
There is one rope on the market (which isn't all that easy to find) called "Black Marlow" - it's a lot like a climber/caver's semi-static, but is less stretchy. You won't find it in a climbing shop because it isn't CE approved for civilian climbing/caving use. (It's insufficiently stretchy to meet the EN1891 standard.)
It's made for the military to use for very long abseils and other gun-toting "hut hut hut hut" type activities. Still stretches a little bit though.
http://marlowropes.com/defence-products-1/abseilclimbing/abseil-rope.html
Commercial camera rigs ('Skycam' type things) usually use something like Vectran. Eg:
http://marlowropes.com/film-a-theatre-prod/v12.html
Rather expensive.
Otherwise, you could perhaps look at using a steel wire rope. Say about 6mm ish, maybe 4mm. Awkward to handle, surprisingly easy to kink, ideally needs to be terminated with clamps ('dogs'/wedge sockets/Strandvise/Reutlinger, etc... ) rather than simply tying a knot, and if you're using climbing pulleys it'll probably eat your sheaves. But it is un-stretchy and relatively cheap.
(And it will still sag some in the middle of a 100m span.)