Keilim, Chapter 24, Mishnah 10. This chapter is built on a single elegant pattern: for one type of utensil after another, the Mishnah announces that there are three of them, and then sorts them into three categories of tum'ah. One version of the utensil is fit to be sat or lain upon, and so it can receive tum'at midras, the tum'ah transmitted by a zav or a niddah pressing their weight upon it. A second version is not made for sitting, but it is a genuine keli with a receptacle, and so it can receive ordinary tum'ah, such as tum'at met, corpse tum'ah. And a third version is neither a seat nor a receptacle, and therefore remains completely tahor. Our mishnah applies this threefold division to mats.
The Mishnah opens: "Shelosha mappatzim hen", there are three kinds of mats.
"Ha'asuy lishivah, tamei midras": a mat that was made to sit upon is susceptible to tum'at midras. Since a person's sitting is precisely the purpose for which this mat was fashioned, it has the status of a seat, and a zav or niddah who sits upon it renders it a midras.
"Shel tzava'in, tamei tamei met": the mat of dyers. Dyers would spread the garments they were working on out upon such a mat. This mat is fashioned with a raised rim running around its edge, so that it holds and contains what is placed inside it. That rim makes it a keli with a receptacle, and a keli with a receptacle can contract tum'at met and the other forms of ordinary tum'ah. What it cannot contract is tum'at midras, because no one lies or sits on a dyer's mat; it was never made to bear a person's weight, and only something designated for sitting or lying can become a midras.
"Veshel gitot, tahor mikelum": the mat employed at the presses, spread out over the fruit as the wine or the oil is extracted, carries no tum'ah of any kind. Being perfectly flat, without any raised edge or cavity, it holds nothing at all and therefore does not qualify as a keli, and whatever is not a keli is beyond the reach of tum'at met. Nor was it ever intended to support a person who sits or reclines, so the category of midras is equally irrelevant to it. Both roads to tum'ah are closed, and this mat remains outside the framework altogether.
Three mats, then, woven perhaps of similar material and looking much alike, yet halachically worlds apart. The first is a seat, and therefore a midras. The second is a vessel, and therefore susceptible to corpse tum'ah. The third is neither, and therefore remains pure. As so often in Masechet Keilim, everything turns not on the substance of the object but on the purpose its owner gave it.