My understanding of a coulis is that it is classically based upon cooked ingredients anyway (meat juices combined w/ a puree of meats). As I've seen it bandied about lately, the meaning has changed a bit, being more like a puree of fruits and such.
Were you to cook it, I would think that might end up as a reduction (whould you cook it that long). By adding syrup you could get a glaze.
The etymology of coulis(from the Latin) simply points to "strain". The question thus becomes, what of a coulis if that coulis is then bastardized...? My own (unprofessional) opinion is that so many terms can be used to described various sauces that there is inevitable overlap. Coulis, reduction, jus, gravy, broth, puree, sauce, etc have very blurry lines between them in many practical cases. I would utilize the term that is most recognizable by the patron as long as that term's besic definition was not explicitly compromised.
But what the heck do I know ?
well then, specifically, I wish to roast yellow peppers, and then puree, strain, and then reduce with maple syrup, butter, and a bit of cream (Im trying to make a menu, just for fun) and I am doubtful that this finished product would qualify.at any rate, thanks for the def. and I would like any more opinions/suggestions as of what this would be so I know what to call it.
Your first bit of text is a perfect description of how to make a coulis. The end product should be smooth and I believe this is the most important factor to consider when referring to a sauce as a coulis.