The Prophet (peace be upon him) prohibited `Ali from being married to his daughter and the daughter of Abû Jahl at the same time. He said:
“The daughter of Allah’s Messenger will not be together with the
daughter of Allah’s enemy.”
It can be understood from the context of this hadîth that the Prophet (peace be upon him) had placed a condition on 'Alî not to marry any other woman beside Fâtimah. We can deduce this from what the Prophet’s (peace be upon him) said about his other son-in-law (Abu Al-'As bin Ar-Rabi', the husband of his daughter Zaynab) keeping his promise not to marry a second wife: “He spoke to me and he was truthful and promised me and fulfilled his promise.”
Ibn Hajr observes in Fath al-Bârî (7/86):
The words “He spoke to me and he was truthful” could be that he made a
promise on himself not to marry another woman beside Zaynab. And the
same was done by 'Alî. Otherwise, it could be that 'Alî had forgotten
that condition and that is why he proceeded with that engagement to
the second woman. Or, it could be that he assumed the condition did
not apply to him since he did not pronounce it himself. However, he
should nevertheless have respected this condition as something
understood, and that is why the Prophet (peace be upon him) blamed
Ibn al-Qayyim writes in Zâd al-Ma`âd (5/117-118):
If a man agrees to the condition that he will not marry a second wife,
he is obliged by that condition. If the man breaks his promise, the
woman will be entitled to terminate the marriage contract.
It is mentioned in the hadîth that what took place is hurting Fâtimah
and therefore hurting him. It is known for sure that the Prophet
(peace be upon him) let 'Alî marry his daughter Fâtimah on the
condition that he does not hurt her or her father, even if that is not
mentioned in the marriage contract. The Prophet (peace be upon him)
brought up mention of his other son-in-law to incite 'Ali to do the
same.” The Prophet’s reproach of `Ali was on account of 'Alî’s
heedlessness of this condition.
And Allah knows best.
Source: Implicit condition not to marry a second wife
This is the Sunni view.