Rabbeinu Tam, France, 12th c., as quoted in Tosafot R. Yehudah Sirleon on Berakhot 47b.

..And the reason that a minor and a slave and a woman may come up to the Torah, even though they
are exempt from the study of Torah, is because the Torah scroll is for hearing. And their blessing is not
in vain, because they do not say "who has sanctified and commanded us regarding Torah," but rather
"who has chosen us...and who has given us."

Beit Habehirah Megillah 24a, R. Menahem Hameiri, Provence, 13th-14th c.

...That which we have taught, "A minor reads from the Torah," the reason for this is that the purpose of Torah reading is that the people hear it, and it is not a bona fide mitzvah such that we would apply the rule , "Anyone who is not obligated in something cannot fulfill the obligations of others..."

Ran Megillah 23a (13a in the Rif's pagination), R. Nissim b. Reuven, Spain, 14th c.

All count towards the quorum of 7, even a woman even a minor. This means: they come up to complete [this

number], but they may not all be minors or women; since they are not obligated, they cannot entirely fulfill the obligations of others.

Beit Yosef Orah Hayyim 53

And so wrote the Rambam...and one whose beard has not filled out, even though he is a great sage should not be a prayer leader because of the honor of the community...according to this, if the community wishes to waive its honor, it seems they have the power to do so. But from the words of the Rosh...it seems that even if the community were to waive its honor, one should not appoint such a person as leader...

Bah Orah Hayyim 53

In my humble opinion, even for Rambam and Rashba the community cannot waive its honor, because the meaning of "because of the honor of the community" is not that we don't do something because it is disrespectful to the people present such that they could waive the concern, rather, it means that it is not fitting for the community that they should send before the Exalted One a lowly person to represent the community...the matter is simple: once the sages established something out of a concern for the honor of the community, the community has no right of waiver. And as further proof of this, were it true that the community could do so, what effect would there be to any of the regulations borne out of a concern for the community's honor, such as not rolling a Torah scroll...if a community is permitted to waive its honor, then every community will do so!

Maczhor Vitry

Regarding 10 people who have prayed everything and have heard kedushah and barkhu...they can count towards another quorum for one who has not yet prayed...and even one of those who has prayed already can repeat the Amidah to fulfill the obligation of the one still obligated. And my master provides support for this ruling from the fact that though the community prays the Amidah individually, the leader repeats it in order to say kedushah. We see, therefore, that those who already prayed count towards the quorum on account of the kedushah alone. Someone challenged this reasoning and said: Perhaps, in your example, they are only counted towards the quorum because they have not yet heard kedushah? They are therefore still obligated and can therefore count in the minyan! My master (Rashi) responded: We do not find anywhere in the Talmud an obligation to hear kedushah; rather, it is dear to us and it cannot be said in a group of less than 10.

Responsa Havvot Yair #222

Question: A strange thing happened in Amsterdam and was well publicized there. A man died without a son and he ordered before his death that 10 men learn every day in his house for 12 months and after their learning his daughter should say kaddish...and the leaders of the community did not object. Even though there is no evidence to forbid such a thing, for women are also commanded to sanctify the Name and there is also a quorum of males who are called "bnei yisrael"...nonetheless, we should worry that by such an act Jewish customs will be weakened...and everyone will build an altar of his own according to his own theories...therefore in this case, where the act is public we should protest.

Siddur Rav Sadia Gaon

If the community prays these three tefillot-The measure of a community for this being ten males who have reached puberty...

R. Manoah Provence, 13th-14th c. This ruling requires consideration...This matter is not explicit in the gemara, but nonetheless it is the law...for it is written, "bless in makheilot", and women are not called a kahal." And we hold similarly with regard to prayer, in which women are obligated, but nonetheless they do not form the quorum of 10, and they as a group on their own do not say kaddish or kedushah, for any davar shebikdushah cannot be said in a group of less than 10, since it is written "And I will be sanctified in the midst of bnei yisrael" and not bnot yisrael. And edah also applies only to males, because the spies were men. And since a davar shebikdushah cannot be said in a group of fewer than 10, and the restriction on mentioning the Name in zimun in a group of fewer than 10 is because this act is a davar shebikdushah, women are thus excluded...and further, common sense tells us that they should not conduct zimun with the Name, because they do not have the intellectual capacity to magnify and exalt the name of the Holy and Blessed One as men do...

Words of Rabbenu Tam in Tosafot Rabbenu Yehudah Sirleon on Berakhot 47b

And I add [to the list of those who count towards a minyan] even an infant in his cradle, for God's presence dwells among all groups of ten, for when the principle of a quorum of ten is learned from the verse "I will be sanctified," no distinction is made between minors and adults. But there must be nine adults, because more than one [minor] can not be counted, as it is taught with respect to a slave, for [with more than one minor] there is insufficient honor for heaven. And a slave also comes under the principle "I will be sanctified," for God's presence dwells among all who are obligated in commandments and members of the covenant. This ruling, that they may count towards a quorum, is only when an adult Jew is blessing, but this minor or slave cannot fulfill the obligations of others...for one not obligated in something cannot fulfill the obligations of others. That a minor, slave or woman, none of whom is obligated in the study of Torah, may be called to the Torah as part of the seven aliyot is due to the fact that a Sefer Torah is for hearing. And their blessing is not in vain, for they do not say "who has sanctified us and commanded us" but "who has chosen us and who has given us"

Levush OH 55:4, R. Mordechai Yafeh, Poland, 16th c. Neither a slave not a woman nor a minor may count towards the minyan, because they are not obligated in mitzvot. And some permit joining 9 adults with 1 minor, since the minor will eventually become obligated...

Words of Rabbenu Tam in Tosafot Rabbenu Yehudah Sirleon on Berakhot 47b

And I add [to the list of those who count towards a minyan] even an infant in his cradle, for God's presence dwells among all groups of ten, for when the principle of a quorum of ten is learned from the verse "I will be sanctified," no distinction is made between minors and adults. But there must be nine adults, because more than one [minor] can not be counted, as it is taught with respect to a slave, for [with more than one minor] there is insufficient honor for heaven. And a slave also comes under the principle "I will be sanctified," for God's presence dwells among all who are obligated in commandments and members of the covenant. This ruling, that they may count towards a quorum, is only when an adult Jew is blessing, but this minor or slave cannot fulfill the obligations of others...for one not obligated in something cannot fulfill the obligations of others. That a minor, slave or woman, none of whom is obligated in the study of Torah, may be called to the Torah as part of the seven aliyot is due to the fact that a Sefer Torah is for hearing. And their blessing is not in vain, for they do not say "who has sanctified us and commanded us" but "who has chosen us and who has given us"