Gemara

2a (Mishnah - Beis Shamai): Until when is a child exempt from Re'iyah (even mid'Rabanan)? He is exempt until he can ride on his father's shoulder from Yerushalayim to Har ha'Bayis;

Beis Hillel say, he is exempt until he can hold his father's hand and walk from Yerushalayim to Har ha'Bayis.

5b - Question (R. Zeira): Who brought the child until Yerushalayim?

Answer (Abaye): His mother brought him to Yerushalayim. She is obligated to go there for Simchah.

Question (Rebbi): Chanah did not go to the Mishkan for the Regel until weaning Shmuel (after two years). According to Beis Shamai, since Shmuel could have ridden on his father's shoulder, Elkanah was obligated to bring him!

Counter-question (Avuha or Abaye): Why didn't Chanah herself go to fulfill her obligation of Simchah?

Answer to both questions: Chanah saw that Shmuel was very delicate, and she feared that the journey would weaken him.

6b - Beraisa - R. Yosi ha'Gelili: The Mitzvah of Simchah applies to men and women.

Rosh Hashanah 6b - Question (R. Zeira): Does Bal Te'acher apply to women?

Since she is exempt from Re'iyah, she is exempt;

Or, since she is obligated in Simchah, Bal Te'acher applies to her?

Abaye: Since she is obligated in Simchah, surely Bal Te'acher applies to her!

Question: Abaye himself says that (she is exempt from Simchah, and) the Mitzvah is for her husband to Mesame'ach her!

Answer: He says, according to you (R. Zeira) she is obligated in Simchah, surely Bal Te'acher should apply!

Pesachim 109a (Beraisa - R. Yehudah): "V'Somachta b'Chagecha" - one must make his household rejoice on the festival. He gives to men what makes them rejoice, and to women what makes them rejoice.

(Rav Yosef - Beraisa): Women in Bavel rejoice over colored clothing; women in Eretz Yisrael rejoice over ironed linen clothing.

Beraisa #3 - R. Yehudah ben Bava: When the Mikdash stands, one fulfills Simchah only by eating (Kodesh) meat - "V'Zovachta Shelamim...V'Somachta";

Nowadays Simchah is only with wine - "V'Yayin Yesamach Levav Enosh".

Kidushin 34b - Question: We should learn from Simchah that women are obligated in Mitzvos Aseh sheha'Zman Gerama!

Answer (Abaye): A woman herself is not obligated in Simchah. Rather, her obligation is on her husband.

Question: A widow has no husband. The Mitzvah must be on her herself!

Answer: It is incumbent on her neighbor.

Question: We should learn from Hakhel that women are obligated in Mitzvos Aseh sheha'Zman Gerama!

Answer: Matzah and Hakhel are Shenei Kesuvim (obligating women), so we do not learn to elsewhere.

35a - Question: R. Yehudah holds that we learn from Shenei Kesuvim. Why doesn't he learn to elsewhere?

Answer: Matzah, Simchah and Hakhel are Sheloshah Kesuvim that obligate women. (All agree that we do not learn from Sheloshah Kesuvim.)

Rishonim

Rambam (Hilchos Chagigah 1:1): The Mitzvah of Simchah on festivals is to offer Shelamim in addition to Shalmei Chagigah. Women are obligated in this.

Ra'avad: She is not commanded about the Korban. Rather, the Mitzvah is for her to rejoice with her husband. She goes with him (to Yerushalayim) and he is Mesame'ach her.

Kesef Mishneh: The Gemara (Chagigah 6b) says that a woman is commanded in Simchah. Rashi says that we learn from "V'Somachta Atah u'Veisecha". Abaye teaches that her husband is commanded to Mesame'ach her. R. Tam explains that he lets her eat from his Shelamim. One cannot fault the Rambam for not elaborating.

Lechem Mishneh: The Ra'avad holds that her husband has no obligation to give her Shelamim to eat. Rather, he brings her to Yerushalayim and is Mesame'ach her (in other ways).

Ri Korkus: Tosfos proves from Chagigah (6a) said that a woman must go to Yerushalayim for the sake of Simchah. The Gemara says that she brings her child to Yerushalayim, for she is obligated to go there for Simchah. This shows that she must eat Kodshim. The Gemara (Pesachim 109a) says that a man is Mesame'ach his wife with linen garments. This is nowadays. Perhaps the Rambam holds that if there a single woman has no man to Mesame'ach her, she herself is obligated. However, the Gemara (Kidushin 34b) said that we do not learn from Simchah that women are obligated in Mitzvos Aseh sheha'Zman Gerama because she herself has no Chiyuv of Simchah. Perhaps the Rambam relies on the Beraisos that connote that she herself is obligated; only Abaye holds that the Mitzvah is on her husband. In the conclusion (Kidushin 35a) we say that Matzah, Simchah and Hakhel are Sheloshah Kesuvim that obligate women, so everywhere else women are exempt from Zman Gerama. This is unlike Abaye. Even though this was according to the opinion that we learn from Shenei Kesuvim, the Sugya leans against Abaye. In Rosh Hashanah (6b), the Gemara asked why Abaye challenged R. Zeira, since Abaye himself holds that women are exempt from Simchah. This shows that R. Zeira argues with Abaye. Also, since the Gemara based the question on Abaye's teaching, this shows that it is not difficult for us, i.e. we hold that she is obligated in Simchah.

Here, we could have said that the Rambam merely cites the Beraisa verbatim. However, in Hilchos Ma'aseh ha'Korbanos (14:14) the Rambam rules that Bal Te'acher applies to women. This shows that he rules like R. Zeira. The Rambam could agree with Tosfos (brought below) that if she has a husband, she is Yotzei with his Shelamim. However, if she is single, she herself must bring Shelamim. The Gemara connotes that the opinion that opposes Abaye holds that women are always obligated. The Rambam did not specify, but it seems that he holds like this.

Rambam (Hilchos Ma'aseh ha'Korbanos 14:14): Bal Te'acher applies to men and women.

Lechem Mishneh: This shows that the Rambam rules like R. Zeira, against Abaye. This is difficult for the Kesef Mishneh, who explained (Chagigah 1:1) that the Rambam rules like Abaye. Also the Ra'avad there rules like Abaye. I do not know why the Ra'avad did not comment here.

Avi Ezri (Chagigah 2:10 DH uv'Perek 1): In Sefer ha'Mitzvos (Aseh 54), the Rambam writes that Simchah is to offer Shelamim in addition to Chagigah. It is also a Mitzvah to get new clothing and to have foods that give Simchah, i.e. meat and wine, or fruits and sweets for women and children. The Chiyuv of women pertains only to the Korban. The Rambam rules like Abaye, who says that the Chiyuv for other aspects of Simchah is on her husband. The Gemara in Kidushin asked from the other aspects, for we cannot learn from a Chiyuv Korban to Mitzvos Aseh sheha'Zeman Gerama.

Rashi (Kidushin 34b DH bi'Shruyah): Abaye himself says that women are exempt from Simchah! Regarding a poor widow, her neighbor is commanded to Mesame'ach her with his food and drink, and with linen garments.

Tosfos (Kidushin 34b and Rosh Hashanah 6b DH Ishah): Abaye himself says that women must go to Yerushalayim for Simchah! Rather, he teaches that her husband is obligated to take her to Yerushalayim, and he must bring Shelamim and give to her to eat from them. Simchah through food and drink and nice garments is only when there is no Mikdash, or when it is impossible to eat Shalmei Simchah, e.g. when the first day of the Regel is on Shabbos.

Rambam (Hilchos Yom Tov 6:17): Even though the verse refers to Shelamim, it also encompasses rejoicing in things that delight men, women and children.

Sefas Emes (Yoma 3a DH b'Tosfos): The Rambam (Chagigah 1:1,3) holds that the Mitzvah of Simchah of eating Shelamim must be fulfilled once during the Regel. Nevertheless, the Mitzvah of Simchah of nice clothes and wine applies the entire Regel. Tosfos (Yoma 3a DH Pazer) holds that there is a Mitzvah to eat Shalmei Simchah every day of the Regel. Whenever this cannot be fulfilled, one fulfills Simchah through nice clothes and wine.

Rambam (18): One buys nice clothing and ornaments for women according to his means.

Ba'al ha'Ma'or (Rosh Hashanah 1a DH Bo'i): Abaye holds that a woman's obligation of Simchah is on her husband, i.e. he must cajole her to come to Yerushalayim. The Gemara asked why Chanah was not persuaded. The text says that Avuha, i.e. Rebbi's father R. Shimon ben Gamliel, challenged Rebbi. It cannot be Abaye, who was not in Rebbi's generation.