Whether you need/want to adjust the outhaul on different points of sail or
wind strengths depends on a number of factors. And it is not related to being on a
monohull, so generally ignore those posters.
1) If your main is made of non-stretch membrane or laminate, you can set and ignore the outhaul. If you want ultimate performance, ease one or two cm for broad reaching and downwind, and tighten one or two cm for reaching and upwind.
2) If your main has full battens, regardless of the material it’s made from, you can ignore the outhaul. It would only affect the portion of the main under the lowest batten, so who cares?
3) If your main has partial or no battens (very unlikely as you don’t have a
furling main and why have a relatively performant cat with no roach?) then you will want to adjust your outhaul.
Just in case, lead your outhaul forward to a clutch or jammer that is inline, or can be lead to a winch. Then try adjusting it and see what difference it makes to the shape of the
mainsail and to
boat speed. I’m pretty sure that you’ll set it and forget it - on a large cat the performance impact of outhaul adjustment is absolutely dwarfed by things like batten tension, sheet tension and traveller position.
On our boat, the three reef lines and the outhaul all come out of the front end of the boom through jam cleats and sheaves that direct them down to the
deck. For adjustment they can be individually led around a 180* turning block at the base of the mast and up to one of the mast winches (one on either side of the mast). In 3 years with membrane
sails we haven’t touched the outhaul except to initially set it to match the
depth curve of the first batten. YMMV