HA'ARA'AH IS CONSIDERED LIKE BI'AH [Ha'ara'ah]
Gemara
54a (Mishnah): Whether the Yavam did only Ha'ara'ah (... he acquired her).
(Ula): We know that Ha'ara'ah is considered like Bi'ah from "V'Ish Asher Yishkav Es Ishah Davah... Es Mekorah He'erah".
Question: This discusses a Nidah. What is the source for other Arayos?
Answer (R. Yonah): "All these abominations" equates all Arayos to Nidah. Just like Ha'ara'ah is like Bi'ah regarding Nidah, also regarding all Arayos.
Regarding homosexuality it says "like one lies with a woman" (in which Ha'ara'ah is considered like Bi'ah).
(Rava): A verse teaches about Ha'ara'ah regarding aunts. R. Yonah's Hekesh teaches this, so this verse is free to teach that Ha'ara'ah to an animal is like Bi'ah.
Regarding a Shifchah Charufah it says "Shichvas Zera" (a full Bi'ah, which can lead to semen). This implies that other Chayavei Lavin are liable for Ha'ara'ah.
We learn Chayavei Lavin of Kehunah from a Gezerah Shavah "Kichah-Kichah" (from Chayavei Kerisos).
We learn from Chayavei Aseh from a Gezerah Shavah "Bi'ah-Bi'ah" (from Chayavei Lavin).
Amora'im (49b) argue about whether Yevamah l'Shuk is a Lav or an Aseh. In either case, we learned that Ha'ara'ah is like Bi'ah.
We learn that Ha'ara'ah is like full Bi'ah to acquire a Yevamah from "Bi'ah-Bi'ah".
We learn that a woman is acquired to her husband through Ha'ara'ah from "Kichah-Kichah".
(Shmuel): Ha'ara'ah is Neshikah (touching of the genitals). This is like one who puts his finger on his mouth. Perforce, it will make some indentation.
(Rabah bar bar Chanah citing R. Yochanan): The Torah is Mechayev for full Bi'ah with a Shifchah Charufah. This is entrance of the crown.
Question (Rav Sheshes - Beraisa): He is liable only for a Bi'ah of Miruk.
Suggestion: This is when he fully enters the Ever (or empties the Ever of its semen)!
Answer: No, he fully enters the crown.
(Rav Dimi and Ravin, citing R. Yochanan): Ha'ara'ah is the entrance of the crown.
Question: They certainly disagree with Rabah bar bar Chanah. Must we say that they disagree with Shmuel?
Answer: No. From Neshikah until entrance of the crown they call Ha'ara'ah.
(Rav Shmuel bar Yehudah citing R. Yochanan): Ha'ara'ah is the entrance of the crown. Full Bi'ah is literally full Bi'ah. Less than this is only Neshikah, and one is exempt for this.
He disagrees with Shmuel.
Rishonim
The Rif and Rosh (5:3,4) bring our Gemara.
Question: Our Gemara says that that a woman is acquired to her husband through Ha'ara'ah. Kidushin (10a) asks whether the beginning or end of Bi'ah acquires. This determines the law of a woman who accepted Kidushin from David while having Bi'ah with Levi l'Shem Kidushin, between Ha'ara'ah and full Bi'ah. Rava answers that the end acquires, for a man intends for this!
Answer #1 (Rif): Our Gemara discusses Bi'ah after Kidushin without Chupah. It acquires for all matters of Nisu'in, e.g. inheritance and Tum'ah (if she dies). Since he already has a Kinyan in her, Ha'ara'ah suffices to finish it, just like it suffices for Yibum.
Rejection (Rosh): Our Gemara learns from "Kichah", which is written regarding Kidushin!
Answer #2 (R. Shimshon, cited in Rosh): If he did only Ha'ara'ah, it acquires. If he did full Bi'ah, he intends to acquire through the end.
Answer #3 (Nimukei Yosef DH Gemara): If he did full Bi'ah but said that he intends to acquire through Ha'ara'ah, he acquires through Ha'ara'ah. Yibum does not depend on his intent, so in any case he acquires through Ha'ara'ah.
Answer #4 (R. Tam, brought in Tosfos Yeshanim 55b:1): In Kidushin we ask if the beginning or end of Ha'ara'ah acquires. This is like the opinion that Ha'ara'ah is entrance of the crown. According to the opinion that it is Neshikah, one cannot distinguish the beginning from the end.
Rambam (Hilchos Isurei Bi'ah 1:10): If one enters only the Rosh of the crown, this is Ha'ara'ah, like it says "Es Mekorah He'erah". Entering the Ever is full Bi'ah. Regarding every forbidden Bi'ah, Ha'ara'ah is like full Bi'ah. Even if there was no semen and he withdrew immediately and did not finish, once he entered the Rosh of the crown they are Chayav Misah or Kares or lashes or lashes mid'Rabanan.
Magid Mishneh (DH Gemara): The Halachah follows R. Yochanan against Shmuel.
Perush ha'Mishnayos (Yevamos 6:1): Ha'ara'ah is entrance of the entire crown. From touching (of the genitals) until entrance of the crown is Neshikah.
Noda bi'Yehudah (2:EH:23 DH v'Atah Nashuvah): The Rambam calls the part of the crown towards the body the 'Rosh'. It follows that also in the Mishnah Torah he requires entering the entire crown.
Question: The Gemara (Yevamos 20b) said that Chachamim decreed not to do Yibum with Chayavei Lavin, lest one have a second Bi'ah, which is forbidden. Since one acquires through Ha'ara'ah, even completing the Bi'ah is forbidden!
Answer (Ran Kidushin 6a DH Garsinan): The entire Bi'ah is considered Bi'as Mitzvah and is permitted, for Yibum is to continue the name of the Mes. Therefore, Yibum requires a Bi'ah that can lead to children. Even though the first Bi'ah normally does not produce children, it happens sometimes.
Poskim
Shulchan Aruch (EH 6:9): Whenever Bi'ah makes a woman a Zonah, she becomes a Zonah from Ha'ara'ah.
Shulchan Aruch (20:1): Once one does Ha'ara'ah to Ervah, i.e. he enters the crown, he is liable.
Taz (5:2): On the bottom of the crown, the entire region from where it narrows is the crown. Therefore, anything past Neshikah is Ha'ara'ah.
Question #1 (Beis Shmuel 3): The Gemara (Reish 56a) says that 'mi'Kan v'Eilach' (less than entering the crown) is Neshikah. Rashi (DH mi'Kan) says that this is from entering the crown and below. According to the Taz, on bottom there is nothing past the crown! Even the Taz must agree that one is not liable unless he enters the top of the crown.
Question #2 (Noda bi'Yehudah ibid., DH Isa): The Gemara asked a contradiction of Diyukim. According to the Taz, we could have answered that both are true: Shifchah Charufah requires full Bi'ah, Chayavei Kerisos require only entrance of the end of the crown, and Chayavei Lavin require full entrance of the crown! It is difficult to say that the Gemara felt that it was unreasonable to distinguish between part of the crown and the entire crown. Also, Rabah bar bar Chanah obligates for Shifchah Charufah for entering the crown, i.e. Miruk (the entire crown). Presumably, whenever we refer to entering the crown it refers to the same thing.
Shulchan Aruch (33:2): One who is Mekadesh through Bi'ah intends to acquire through the end of Bi'ah. Therefore, if she accepted Kidushin from a different man before full Bi'ah she is Mekudeshes to the latter man. If the Mekadesh separated immediately after Ha'ara'ah or specified that he intends to acquire through Ha'ara'ah, he acquires immediately.
Shulchan Aruch (166:7): A Yevamah is acquired even through Ha'ara'ah.