Swan reminds me of Michael Corleone, very smart always a step ahead. While Ajax reminds me of Sonny Corleone a hot head fighter but not very smart.

I have a theory, though it may be far-fetched. I believe Ajax knew the woman was a cop, 'cause it was kind of obvious. He was ill-tempered and a brawler, but not stupid. The odds of making it home unscathed from the other gangs were slim, so the safest bet was to get himself jailed. Knowing what kind of guy he is, he still won't take any beep from the police even when "giving himself up".

Huh?
"[E]ntrapment is a practice whereby a law enforcement agent induces a person to commit a criminal offense that the person would have otherwise been unlikely to commit."
Her words to him did not request or even encourage any acts of violent sexual assault. She made a broad and open ended request. He could have responded to that line in any number of ways which did not involve violent sexual assault.
If the undercover police woman had said, "Show me how rough you can be, and ignore me when I tell you to stop." then maybe it could be entrapment. But just being in a sketchy place and being sexually encouraging should not be an open invitation to or legal excuse for brutal sexual assault.

Entrapment is when a police officer induces someone to commit a crime. For example, an officer asks someone to buy drugs for them and later arrests them for that. In other words, the police officer creates the crime, in a sense.
In this case, the officer didn't induce him to rape her. She was just sitting there and he approached her. If anything, she invited him to consensual sex. But when he went forward after she said stop, it became his crime.

Yes! OMG I thought the same thinghe is constantly talking about "goin' beep he uses that phrase at least three times. And of course the famous "I'm gonna shove that baseball bat up your *** like a popsicle stick" threat. He definitely is obsessed with homosexuality.

The dialogue between them makes it very clear that, though the woman consented to sex, Ajax didn't
want
consensual sex; what he wanted was to rape her, to hurt her. His fate is entirely his own fault, and completely deserved.
(FWIW, incidentally, I always assumed Ajax was a deeply-closeted, self-loathing gay man, and that his brutal treatment of the policewoman was an attempt to reaffirm his sense of his own masculinity - notice how awkward and nervous he is with her before he regains his confidence by getting violent.)

The policewoman was played by Mercedes Ruehl. She won the Academy Award for Best Supporting Actress in 1992 for "The Fisher King" and a Tony Award for her performance in "Lost in Yonkers" in 1991.

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At least he got to rejoin his friends after some time in jail. How much time do you think he got?

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"Your days of playing in the park are over for a while"
She was a lure for a serial rapist that had been attacking women in that park.
So when Ajax starts getting rough she bags him for being the guy they are after.

Entrapment was the only way the NYPD could get a conviction back then.

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Honestly I thought the same thing. The women instigated it. Now he was not trying to rape her either. She was acting willing and he just liked it rough. That's not excusing the act but rather saying he was set up like a mother beep
I disagree with that assessment, michaeluk26. I think that Ajax was the one who institated it. Ajax set himself up when he wanted to go "get some exercise", despite the fact that his fellow Warriors gang members told him that he should wait, that there were plenty of women back home in Coney Island.
When Ajax tried to have sex with the woman on the bench, he had absolutely no idea that she was a cop. He was surprised and angry when he got arrested. Ajax, imho, acted
very
stupidly, and he
deserved
to get into trouble and get arrested for his actions and behaviors..

It would still legally count as entrapment, cause a cop is not allowed to manipulate a person into assaulting them, then making an arrest.
It would still fall under entrapment laws, and Ajax would most likely go free.

Stupid, psychotic, and constant need to overstate his macho man masculinity by calling out everyone for "going f@?g*t" I'd say he had a couple date rapes under his belt

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Ajax is clearly represented as stupid and psychotic throughout the story. He may or may not have been entrapped but I'm intrigued by this post. When did Swan admit he had made a mistake in letting Ajax wander off by himself?
"Your next challenge is always your biggest." Joe Namath

Yep especially in a despotic future where everything is supposed to be run down. Swan to his credit admitted he made a mistake and should pull ranked over Ajax and told him to move along.

Swan did say "You never were very smart" A chick alone in Central Park at night - Ding ding dingRings undercover to me
YOU MADE ME PLAY SECOND BASE!

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Honestly I thought the same thing. The women instigated it. Now he was not trying to rape her either. She was acting willing and he just liked it rough. That's not excusing the act but rather saying he was set up like a mother beep
Haters gonna hate

Exactly, he was not entrapped. When a woman says "stop" or "no" the man has to stop. He approached her and when she told him to stop and he did not it became assault.
People who love to say a man was entrapped or set up need to remember, a man can always walk away or stop.