Halakhah sur Kéilim 1:2

From the laws of the commandment is that which they, may their memory be blessed, said (Mishnah Kelim 1:2) that a carcass is a primary source (av) from the primary sources of impurity; and that a kazayit of its flesh makes a man and vessels impure by touching, and a clay pot from its hollow; and makes a man impure from carrying to make [his] clothes impure. And it is one whether it is a permitted beast or animal or a forbidden one that died - the flesh of all of them transfer impurity with a kazayit. And the slaughter of a pure beast or animal purifies them and they do not transfer impurity afterwards. And even the slaughter of non-sacred [animals] in the courtyard or consecrated ones outside purifies them from being a carcass. And anything that dies on its own or a disqualification occurred in its slaughter, behold it is a carcass - and like they, may their memory be blessed, said in Chullin 32a, "This is the general principle: All that became disqualified in its slaughter is a carcass; and all that something else caused it to become disqualified, is 'torn' (tereifah)." But slaughter does not purify an impure beast or animal from being a carcass. And hence they are carcasses in any way that they die. And nonetheless, they do not transfer impurity - not them and not the pure ones - until they die completely, and not while they are still twitching. And the rest of its many details are elucidated scattered in the Order of Tahorot, but mostly in Tractate Kelim and Tractate Tahorot (see Mishneh Torah, Laws of Defilement of Foods 1)