Gemara

(Mishnah): For any Mitzvah punishable by Kares if he was Mezid and Chatas if he was Shogeg:

A (regular) individual brings a female goat or lamb. A Nasi brings a male goat. Bulls are brought for a mistaken Hora'ah of Beis Din (that caused most of Yisrael to transgress) or a Moshi'ach (a Kohen Gadol anointed with Shemen ha'Mishchah, which caused himself to sin).

For idolatry, an individual, Nasi or Moshi'ach brings a male goat (a Chatas). The Tzibur (Beis Din) brings a bull for an Olah and a male goat for a Chatas.

Question: What is the source for this?

Answer #1 (Beraisa - Rebbi): We learn from a Gezerah Shavah from "V'Nod'ah ha'Chatas Asher Chot'u Aleha";

It also says "Aleha" regarding Achos Ishto, which is punishable by Kares and Chatas. Here also, we discuss something punishable by Kares and Chatas.

This teaches about the Tzibur. "For the guilt of the nation" equates a Moshi'ach to the Tzibur. We learn an individual and Nasi from a Gezeirah Shavah "Mitzvos-Mitzvos".

(Beraisa): For idolatry they bring only for something punishable by Kares and Chatas.

A Gezeirah Shavah "Einei-Einei" teaches this law for the Tzibur. We learn an individual, Nasi and Moshi'ach from "And if one Nefesh". Each of these is a Nefesh!

"And" teaches that we learn the latter Parashah from the previous one.

Answer #2: Chachamim learn like R. Yehoshua taught to his son, "Torah Achas Yihyeh Lachem la'Oseh bi'Shgagah; Veha'Nefesh Asher Ta'aseh b'Yad Ramah (Es Hash-m Hu Megadef )";

(Regarding Korban,) the entire Torah is equated to idolatry (Megadef), which is punishable by Kares and Chatas.

This teaches about an individual, Nasi and Moshi'ach, for regular sins and idolatry.

Regarding idolatry, "And if a Nefesh" equates the Tzibur to an individual, which is written after it. Regarding other Mitzvos we learn a Tzibur from a Gezeirah Shavah "me'Einei-me'Einei."

Makos 13b - Question: Why does R. Akiva exempt Chayavei Misos from lashes?

Answer #1 (Rava): R. Akiva holds that one is not lashed for a Lav that warns for Misah (since it cannot warn also for lashes).

Question: If so, R. Akiva should likewise exempt Chayavei Kerisus from lashes (the Lav warns for Kares, not for lashes)!

Answer (Rava): Kares does not need a Lav. There is no Lav for Korban Pesach and Milah (circumcision), yet they are Chayavei Kerisus.

Question: Perhaps the Lav (for the other Kerisus) is to obligate a Korban (for Shogeg)!

Support: There is no Lav for Pesach and Milah, therefore one who does not fulfill them does not bring a Korban (Chatas)!

Answer: No, they are exempt because the Torah obligates a Chatas only for transgressions similar to idolatry, i.e. we are commanded to refrain. Pesach and Milah are Mitzvos to do an action.

Answer #2 (to Question 12 - Ravina): R. Akiva learns from "Kedei Rish'aso".

Question: Before Teshuvah there is also Kares. Lashes is a second punishment!

Answer (Ravina): Since he can avoid one punishment (by doing Teshuvah), this is not considered two punishments.

Shevu'os 14b (Mishnah): If a woman told her husband during relations that she became a Nidah, if he withdraws (the Ever) immediately (while it is still in erection), he is Chayav, because withdrawing is pleasurable, just like entrance.

(Rava): If he withdrew immediately he must bring two Korbanos: one for relations with a Nidah, and one for withdrawing.

Rishonim

Rambam (Hilchos Shegagos 1:1): If one transgressed b'Shogeg any Lav with a Ma'aseh punishable by Kares, he must bring a Korban Chatas.

Ri Korkus: The Toras Kohanim expounds that Chatas is only for a Lav with a Ma'aseh with Kares.

Question (Teshuvah R. Akiva Eiger ha'Chadashos CM 9 DH ul'Zeh): The Rambam rules like Rebbi, who says that there is Korban only when there is a Lav. If so, why does the Rambam (Shegagos 2:2) egas obligate a Korban for one who was Mezid about the Lav but Shogeg (did not know) about the Korban? This is like Chachamim (Shabbos 69a)!

Question: If we learn from idolatry, we should say that one brings a Korban only for an Aveirah punishable by stoning!

Answer (Tosfos 9a DH Mah Avodas): We learn only from what is explicitly written there. The Tana holds that Megadef, which the verse says is Chayavei Kerisos, refers to serving idolatry. Chachamim do not learn from idolatry, therefore they do not require a Lav. We exclude Pesach and Milah from Korban because they are transgressed passively, not because there is no Lav. Rebbi holds that there is Kares for Porek Ol, Mefer Bris and Megaleh Panim. He did not teach them with the 36 Kerisos (Kerisus 1:1) because he exempts from Korban because there is no Lav.

Rambam (ibid.): It is a Mitzvas Aseh to bring a Chatas for the Shegegah.

Rebuttal (Ramban Sefer ha'Mitzvos Shoresh 12, 78b): BaHaG does not count a separate Mitzvah for the sinner to bring a Korban, only for the Kohanim to offer it.

Defense (Kin'as Sofrim): According to the opinion that Kohanim are Sheluchim of Yisrael, one could say that it is all one Mitzvah. However, the Ran says that the conclusion is that Kohanim are Sheluchim of Hash-m. Since the sinner and the Kohanim have separate obligations and one cannot fulfill the other's, we must say that they are separate Mitzvos.

Sefer ha'Chinuch (121): It is a Mitzvas Aseh to bring a Chatas for one's Chet. This lowers the spirit of the sinner.

Rambam (4): There are 43 Aveiros for which one brings Chatas Kavu'a. For idolatry, a commoner, Nasi or Moshi'ach brings a female yearling goat. For any of the other 42, a commoner brings a female goat or lamb, a king brings a male goat, and a Moshi'ach brings a Par Chatas that is burned.

Ri Korkus: Kerisus 1:1 lists only 36 Aveiros, and one does not bring Chatas Kavu'a for five of them. The Rambam counts 43 because he counts separately Arayos grouped together in Kerisus. E.g. Kerisos lists 'a woman and her daughter', and the Rambam counts the daughter, mother, granddaughters and grandmothers of one's wife. Regarding idolatry everyone brings the same Korban because 'there is no Chachmah or importance (that warrants special treatment) in the face of (such a terrible offense against) Hashem' (based on Mishlei 21:30).

Tosfos (Shevu'os 17b DH Aval): Even though one brings a Chatas only for Aveiros similar to idolatry, in which we are commanded to refrain, also the Aseh of Nidah is a command not to withdraw (amidst Kishuy) with Hana'ah.

Tosfos (Shevu'os 18b DH Lo): One does not bring a Chatas unless there is a Lav, like we find regarding Korban Pesach and Milah.

R. Akiva Eiger (Teshuvah 2:118): Tosfos on 17b explains according to Chachamim. Tosfos 18b explains according to Rebbi, for the Gemara assumes that Rebbi agrees. Rebbi does not say that when a Lav warns for Korban, there are no lashes. This is because Korban does not require a warning. The Lav is merely a Siman that one brings a Korban for the Aveirah. However, according to Rebbi we should require an Aveirah similar to Achos Ishto (from which he learns Chatas)! Rather, Tosfos holds that the Sugya on 18b is like Ravina, who requires a warning for Korban (unlike Rava).