Gemara

(Mishnah - R. Meir): If Yom Kipur was Shabbos, one can be liable for Hotza'ah (transferring from Reshus ha'Yachid to Reshus ha'Rabim, if he walked outside with the food in his mouth)!

Question: Even if it was not Shabbos, he liable for Hotza'ah on Yom Kipur!

Answer (Rafram): This teaches that Isurim of carrying apply only on Shabbos, but not on Yom Kipur.

Rejection: Perhaps carrying is forbidden on Yom Kipur. R. Meir means, if it was Shabbos and he took the food outside, he is liable for Hotza'ah on Shabbos and Yom Kipur!

Rather, Rafram learned from the following Beraisa;

(Beraisa): "V'Shilach b'Yad Ish Iti" teaches that even a Zar (may send the goat to Azazel), even on Shabbos.

(Rafram): Since a verse is needed to permit on Shabbos (even though we know that it is permitted on Yom Kipur), this teaches that prohibitions of carrying apply only on Shabbos, but not on Yom Kipur.

Rejection: Perhaps carrying is forbidden on Yom Kipur;

The Mitzvah is to send it on Yom Kipur, in spite of the Isur Hotza'ah of Yom Kipur. However, without a verse we would not know that it also overrides the Isur Hotza'ah of Shabbos.

Rafram's teaching is Bedusa (totally wrong).

Megilah 7b (Mishnah): The only difference between Shabbos and Yom Kipur is that the punishment for Melachah on Shabbos b'Mezid is through Beis Din (stoning), and that for Yom Kipur is through Shamayim (Kares).

Eruvin 30b (Beraisa - Beis Hillel): Just like we may Me'arev for an adult on Yom Kipur, we may Me'arev for a Nazir with wine, or for a Yisrael with Terumah.

Beis Shamai: No. An adult was permitted to eat the Eruv before dark (on Erev Yom Kipur), but wine and Terumah are forbidden to a Nazir or Yisrael even before dark!

Shabbos 114b (R. Huna): When Yom Kipur is on Shabbos, Kenivas Yerek (cutting or rinsing vegetables) is forbidden.

(Rav Mana - Beraisa): When Yom Kipur is on Shabbos, Kenivas Yerek is forbidden. It says "Shabason" (cease). This need not teach about Melachah. It explicitly says "Lo Sa'aseh Chol Melachah"! Rather, it forbids Kenivas Yerek.

(R. Yochanan): When Yom Kipur is on Shabbos, Kenivas Yerek is permitted (after Minchah).

Question: The Beraisa forbids!

Answer: Really, Shabason adds an Isur (derived from an) Aseh in addition to the Lav forbidding Melachah on Yom Kipur.

Support (for R. Yochanan - Beraisa): When Yom Kipur is on Shabbos, Kenivas Yerek is permitted (after Minchah).

(R. Yochanan): On Yom Kipur, one may break open nuts and pomegranates after Minchah, due to Inuy.

The household of Rav Yehudah would cut (or rinse) cabbage; the household of Rabah would peel gourds.

Rabah saw that they were starting before Minchah. (To get them to cease,) he told them that a letter came from Eretz Yisrael saying that R. Yochanan forbids.

Rishonim

Rif and Rosh (Beitzah 6a and 1:19): On Yom Kipur we need Eruv Techumim (to leave the Techum) and Eruvei Chatzeros (to carry from one Reshus ha'Yachid to another). We find that Beis Hillel and Beis Shamai agree about this.

Beis Yosef (OC 611 DH v'Chen): This is a flimsy proof. Perhaps the Beraisa discusses Eruv Techumim (which applies even to Yom Tov, but Yom Kipur does not require Eruvei Chatzeros, just like Yom Tov does not)! However, the Rambam and Tur rule like the Rif and Rosh.

Gra (611:2): The Rif is difficult, for there we discuss Eruv Techumim!

Rambam (Hilchos Eruvin 8:4): Just like one may not leave the Techum on Shabbos, also on Yom Kipur. Just like one who Motzi from Reshus to Reshus on Shabbos is liable, also on Yom Kipur. Therefore, we make Eruv Techumim and Eruvei Chatzeros on Yom Kipur, just like on Shabbos.

Rambam (Hilchos Shevisas Asor 1:2): Any Melachah for which one is stoned on Shabbos, he is Chayav Kares for it on Yom Kipur. Any Melachah for which one is Chayav Chatas on Shabbos, he is Chayav Chatas for it on Yom Kipur. Whatever is forbidden on Shabbos, even if it is not a Melachah, it is forbidden on Yom Kipur. If one did it, he is lashed mid'Rabanan, just like regarding Shabbos. Whatever one may not move on Shabbos, he may not move on Yom Kipur. Whatever one may not say or do l'Chatchilah on Shabbos, it is similarly forbidden on Yom Kipur. The rule it, the only difference between Shabbos and Yom Kipur is that one is stoned for Melachah on Shabbos b'Mezid, and on Yom Kipur he receives Kares.

Beis Yosef (DH u'Mah she'Chasav v'Chol): The rule (the only difference...) applies to all laws, both mid'Oraisa and mid'Rabanan.

Rambam (3): Kenivas Yerek is permitted on Yom Kipur from Minchah and onwards. I.e. he removes the moldy leaves, and cuts the rest to prepare it to be eaten.

Magid Mishneh: Rashi holds like the Rambam. Shabbos 73b supports them, for it discusses Kenivah of beets, i.e. detaching them. Others challenged them, for separating bad leaves is a proper Melachah, i.e. Borer! I answer that Borer is only absolute Pesoles (waste), or selecting a species from a different species. Here, it is all one species, and the bad leaves are not absolute Pesoles. Perhaps they can be eaten with difficulty. Therefore, it is forbidden only mid'Rabanan on Shabbos, and it was permitted on Yom Kipur. The Ramban and Rashba explained that Kenivas Yerek is rinsing it. The Yerushalmi and Tosefta permit this.

Gra (DH Lekanev): The opinion of the Rashba and Ran is primary. The Tosefta and Yerushalmi support it, and this cannot be rejected.

Rambam (ibid.): Similarly, one may break open nuts and pomegranates from Minchah and onwards. If Yom Kipur is on Shabbos, it is forbidden the entire day. The custom in Bavel and the west is not to do any of these on Yom Kipur. Rather, it is like Shabbos in every respect.

Magid Mishneh: The Rambam forbids on Shabbos, for the latter Amora'im (Rav Huna) forbid, and a Beraisa supports them.

Gra (OC 611:4): This is difficult, for in Berachos, the Rif (28b), Rambam (Hilchos Berachos 8:10) and all Poskim rule like R. Yochanan against Rav Huna! We follow the latter Amora'im only from Rava and Abaye and onwards. The Beraisa supports R. Yochanan! We must say that in his text, the Beraisa supports Rav Huna.

Magid Mishneh: We forbid before Minchah, for it looks like he does so for the needs of today. Alternatively, perhaps he will come to eat it. After Minchah, it is close to night, so he knows that soon he may eat, so we are not concerned lest he eat now. Chachamim permitted for Agmas Nefesh, i.e. so one can prepare everything and he will not be sad. The Rif did not mention these laws, for the custom is to forbid.

Tosfos (Kerisus 14a DH Ela): Rafram is brought also in Yoma (66b), and there he was not rejected. Divrei Torah are poor in some places (there the Gemara did not explain that he is rejected), and rich elsewhere.

Poskim

Shulchan Aruch (OC 611:2): Every Melachah for which one is liable on Shabbos, he is liable for it on Yom Kipur, just on Shabbos one is stoned, and for Yom Kipur he is Chayav Kares.

Mishnah Berurah (4): This is relevant even nowadays. If one wounded on Shabbos, he is exempt from paying (because he was Chayav Misas Beis Din), even if he was Shogeg, but one who wounds on Yom Kipur must pay.

Shulchan Aruch (ibid.): Whatever is forbidden on Shabbos but one is exempt for it, the same applies to Yom Kipur. Whatever one may not move on Shabbos, he may not move on Yom Kipur.

Beis Yosef (DH v'Chasav): The Semag says that the conclusion is unlike Rafram. The Mizrachi disagreed. He said that the Gemara is a mere Dichuy. I say that if so, the Gemara should not have said that Rafram's law is Bedusa. Rather, the Halachah does not follow him. Eruvin and (Isurim of) Hotza'ah apply to Yom Kipur.

Shulchan Aruch (ibid.): They permitted Kenivas Yerek and to break open nuts from Minchah and onwards when it is a weekday. Nowadays the custom is to forbid.

Beis Yosef (DH u'Mah she'Chasav Ela): Rashi says that Kenivas Yerek is detaching leaves from stalks, so they will be ready to cut (at night).

Taz (1): Rashi says that the Heter for Kenivas Yerek is for Inuy. He sees the food prepared, but he may not eat it.

Magen Avraham (2): We must say that the vegetables are proper to eat raw. If not, they are Muktzeh, for even children would not eat them!

Rebuttal (Bi'ur Halachah DH Lekanev): Perhaps just like Chachamim permitted Kenivas Yerek due to Agmas Nefesh, they permitted also Muktzeh! Some explain that Kenivas Yerek (is removing bad leaves, so) there is concern for Breirah. Muktzeh is no more stringent! R. Mano'ach says that the vegetables can be eaten raw, for if not, cutting it is Tochen (grinding). The Me'iri proposed this, but rejected it, for Amora'im did so with cabbage and gourds, which are not eaten raw. This refutes the Magen Avraham.

Mishnah Berurah (7): The Heter is from Minchah Ketanah (two and a half hours before the end of the day), which is close to night. This is when people normally prepare the evening meal on weekdays, so it looks like he prepares for the night.

Mishnah Berurah (8): We forbid when Yom Kipur is on Shabbos, lest people prepare on a regular Shabbos for the night.

Bi'ur Halachah (DH v'Liftzo'a): The Darchei Moshe brings from Mahara of Prague that one may not remove the food from the nut shell, for this is Dash (extracting). However, a Tosefta permits on Yom Kipur, just like on Shabbos for the sake of Shabbos, and then surely one may remove the food! The Yerushalmi says that they also permitted telling a Nochri to cook for the sake of the night. The Poskim did not bring this. Perhaps this is because we are stringent even about Kenivas Yerek.

Kaf ha'Chayim (13): It is like Dash because it is not to eat immediately. However, for the need of that meal is called immediately. We can say that Chachamim permitted this Breirah mid'Rabanan, as if he will eat immediately.