I would like to suggest that according to Abaye there is no need for a document of divorce to have a valid category of a document (even though the document needs to be written for her sake). Where in the Torah do we have any such thing as valid categories of documents? Where was we find the sages instituted certain provisions for documents, but those are not from the Torah. {In fact, the Rambam wrote that documents of loans are valid only from the words of the sages, not from the Torah.} What I mean is this. We know that the document of divorce needs to be written for her sake. Also, R. Elazar said witnesses that see the handing over of the document cause the divorce to be valid. But R Elazar says nothing about these witnesses needing to see it for her sake. Even R Meir (who said the witnesses on the document cause the divorce to be valid) says nothing about the witnesses needing to be for her sake. However, in Gitin page 86, the Mishna says if two documents of divorce were sent by two different people and got mixed up, the messengers give both to each woman. R Yirmia said this mishna is not like R Elazar and Rashi says the reason is the witnesses do not know for which woman the documents were written. For R Yirmia does hold a requirement of lishma in the giving if the documents. But Abaye said there is no need for the witness to know for which woman each document was written. They only need to see the giving of the documents. I might mention that even R Meir says nothing about the witnesses needing to be lishma. At any rate, I saw that Rav Shach and R Aaron Kotler bring up this idea about the documents needing to have the valid category of a document, but I not know why this is necessary to explain Abaye or R Yirmia. All R Yirmia said was the witnesses need to be lishma.---------------------------------I would like to suggest that according to אביי there is no need for a גט to have a valid category of a document, even though the גט needs to be written for her sake. Where in the תורה do we have any such thing as valid categories of documents? Where was we find the חכמים instituted certain provisions for documents, but those are not from the תורה. {In fact, the רמב''ם wrote that documents of loans are valid only from the words of the חכמים, not from the תורה.} What I mean is this. We know that the גט needs to be written for her sake. Also, ר’ אלעזר said witnesses that see the handing over of the גט cause the divorce to be valid. But ר' אלעזר says nothing about these witnesses needing to see it for her sake. Even ר' מאיר (who said the עדי חתימה כרתי) says nothing about the witnesses needing to be for her sake. However, in גיטין פ''ו ע''א, the משנה says if two documents of divorce were sent by two different people and got mixed up, the messengers give both to each woman. ר' ירמיה said this משנה is not like ר' אלעזר and רש''י says the reason is the witnesses do not know for which woman the documents were written. For ר' ירמיה does hold a requirement of לשמה in the giving if the documents. But אביי said there is no need for the witness to know for which woman each document was written. They only need to see the giving of the documents. I might mention that even ר' מאיר says nothing about the witnesses needing to be לשמה. At any rate, I saw that רב שך and ר' אהרון קטלר bring up this idea about the documents needing to have the valid category of a document, but I not know why this is necessary to explain אביי or ר' ירמיה. All ר' ירמיה said was the witnesses need to be לשמה.----------Later note: Reb Aaron Kotler writes that a document of divorce needs to be established as having the validity of a document, and he derives this from Gitin page 10 side b. There R. Shimon said in the Mishna that gitin (documents of divorce) written in gentile courts are valid, but not gitin written by amateurs. The gemara asks on this, “But they are not in the a category of gitin and kidushin?" Reb Aaron understands from this that gitin need to have a category of a valid document. That is a valid derivation from the question in the approach of R. Meir. However, the gemara answers that R. Shimon is going like R Elazar who holds witness that see the handing of the document of divorce cause it to be valid. In any case, on page 86 R Yirmia and Abaye are discussing the opinion of r Elazar.---------------Another note: I think Rav Shach intends to say that the document of divorce needs the validity of a document, and that this can be established either by witnesses that sign the document or witnesses that see the handing over of the document. However, for the validity of the divorce itself we need the witnesses to see the handing over of the document. This is according to Rabainu Tam. However, to the Rambam, witnesses that sign on the document also can cause the validity of the divorce or even just a handwritten note from the husband as long as there are two witnesses that see it being handed over. But I think it is hard to understand why the witnesses that sign the document can cause it to be valid if in any case we always need any document that comes into court with witnesses to anyway needs further validation by calling these very same witnesses. This is derived from a verse that witnesses are valid only if court hears their testimony from their mouths, not from their writing. According to Reb Aaron Kotler, Abaye would not need any establishment of the validity of the document of divorce itself. This is the argument between Abaye and R. Yirmia.