A genius? I just love studying.

Chapter 90: Grasping the Main Contradiction (Monthly Ticket Bonus)

Consider a short exact sequence 0→A→f(B)→g(C)→0 in the category of Abelian groups. Given A=Z/2Z, B=Z/4Z, C=Z/2Z, and f is induced by an inclusion map, g is a quotient map. Now apply the Hom(-, Z/2Z) functor to this short exact sequence, obtaining the sequence 0→Hom(C, Z/2Z)→Hom(g, Z/2Z)Hom(B, Z/2Z)→Hom(f, Z/2Z)Hom(A, Z/2Z)→0. Determine whether this new sequence is exact, and prove it.

Looking at this homework, Chen Hui was completely immersed in the world of homological algebra.

As the study progressed, even Chen Hui felt a little bit tired, and he could no longer learn it with just one glance as before.

But Chen Hui's thinking is very clear.

This question is nothing more than examining the definition of exactness and the relevant knowledge of group homomorphism.

Just calculate the homomorphisms of each group first, then analyze the interaction between the two induced homomorphisms f and g, and then find their kernels and images, and finally verify the exactness.

This was the first time Chen Hui encountered such a question. Although he had a clear idea, he still started to calculate it on a piece of scratch paper.

Only when he is very familiar with this type of question will he just go through the idea without doing any calculations.

To sum up, sequence xxx is exactly right!

[Your math level increased from level 2 43% to 44%]

Just as Chen Hui was calculating freely, a barrage of comments appeared before his eyes as if it was a natural progression.

Li Hai, who was standing by, was holding a cell phone and was about to say something to Chen Hui. However, after seeing a bunch of inexplicable symbols on the draft paper, he forgot what he was going to do for a moment.

"Li Hai, what are you doing?"

A piece of chalk flew over and hit Li Hai accurately. Liu Xiaohua looked at Li Hai with a murderous look on his face, "Hand over your phone!"

Playing with mobile phone during class time is really disrespectful to her as a teacher.

. .

Li Hai was speechless. The last time Chen Hui took out his phone to check messages, he saw Teacher Liu glance over here.

Teacher Liu didn't say anything at that time.

Why do I have to be hit by a piece of chalk when it’s my turn?
This world is so unfair.

However, he did not listen to Liu Xiaohua and hand over his phone. Instead, he put the phone in front of Chen Hui and said, "Chen Hui, take a look at these comments."

[Girls, I've found out the details of that guy! ]

This is a Xiaohongshu post. The picture attached to the post is the ranking list of the Barbaria Mathematics Competition preliminaries. Chen Hui's eighth position is circled in red.

[His uncle is a delivery man and his aunt is a cleaner.

I suggest that the girls in Chengdu order more takeout. If you encounter this delivery man named Li Tianhua, give him a bad review. Here is the tutorial for giving a bad review... If you have time, you can also order a cleaner on the Gouxi platform, specify Fan Rongrong, choose a remote location, and then cancel the order after she arrives. If you can't cancel it, give a bad review as well. Here is the tutorial...

We must not be lenient when dealing with this kind of cheating and unfair competition. The Jimeis must show no mercy. We must let them know that even if Barbaria doesn't deal with him, we can punish him on behalf of justice. Everyone, join me in this action!]

Looking at the post date, it was posted on June 8th, and several days have passed.

This post has more than 3,000 likes and more than 1,000 comments.

【Haha, I succeeded (screenshot)】

【Jimei is good】

【Messenger of Justice! 】

【And you are our hero! 】

[Wow, Jimei is so lucky, I've placed more than ten orders and haven't met Li Tianhua yet]

【I only ordered three...】

"This isn't a good idea. Even if you suspect Chen Hui, just find evidence of his cheating. Don't hurt innocent people..."

[Please remember that Li Tianhua received this bad review today because of you]

[Under the avalanche, no snowflake is innocent]

[Where is Jimei’s takeaway? I want to go there too]

Have you ever thought about how powerful the children of delivery drivers and cleaners could be? If they could truly dominate the world, why would they still be delivering packages?

Many of the comments featured pictures with the names of Li Tianhua and Fan Rongrong on them. Giving negative reviews to Li Tianhua and Fan Rongrong has become a frenzy.

Although there are people who try to give rational advice, such people are often attacked by countless people or simply ignored. For these people, the truth is not important at all.

boom!
A huge rage burned in my chest.

No wonder my uncle and aunt came back so early these days!

No wonder my uncle and aunt have been looking so gloomy these days. They only force a smile in front of them.

Chen Hui knew that there were many people questioning his remarks online, but he always thought that as long as he showed his absolute strength, these remarks would naturally become a joke, so he never took them to heart.

But he didn't expect that those guys would dare to go so far!
These guys are torturing my uncle and aunt!

When he thought of this, Chen Hui felt his heart bleeding.

"Is this a rebellion?"

Liu Xiaohua, who was standing on the podium, was stunned. She didn't expect Li Hai to be so bold. Not only did he not hand over his mobile phone, he even gave it to Chen Hui to see.

Openly instigating classmates to play with mobile phones in class?

"How dare he?"

She walked down the podium angrily in her high heels, came to the fourth row, grabbed Li Hai's cell phone and put it in front of her. She wanted to see what Li Hai was looking at in class.

"?"

With just one glance, she realized the seriousness of the problem.

"Chen Hui, don't be impulsive!"

Liu Xiaohua put away her phone and said, "Li Hai, Chen Hui, the two of you come with me to find Teacher An."

"Other students, please study on your own for a while."

Chen Hui had calmed down by this time. He knew that being angry would be of no help. The most important issue now was to solve his uncle and aunt's dilemma.

Go find Teacher An.

Teacher Liu's destination coincided with his.

An Chengzhang was correcting homework in the office. He was a little surprised to see Liu Xiaohua and Chen Hui come in.

Logically speaking, even if Chen Hui played with his mobile phone in class, Liu Xiaohua should not have cared.

"Teacher An, look at this!"

Liu Xiaohua handed Li Hai's phone over, only to find that the screen was locked, and then she glared at Li Hai.

Li Hai quickly stepped forward to unlock the phone and handed it to Teacher An.

An Chengzhang picked up the phone curiously, and the more he looked at it, the deeper his frown deepened.

"Teacher An, does our school need to come forward to clarify this?"

Liu Xiaohua asked worriedly. She had also seen the negative comments on the Internet these days, but their thoughts were similar to Chen Hui's. They all knew Chen Hui's strength and knew that Chen Hui would soon make those questioning voices disappear.

So they didn't take too many countermeasures. Now it seems that letting the situation develop is absolutely not an option. The school has the responsibility to protect its students!

An Chengzhang frowned. He was very worried about how effective the school's clarification would be.

Liu Xiaohua certainly understood this, but the school should always do something.

"Teacher An, can you take me to see Principal Zhao?"

At this time, Chen Hui stepped forward and said straight to the point, "Principal Zhao, can you arrange a job for my uncle and aunt at school?"

Chen Hui also knew that Teacher An seemed to have some influence in the school, otherwise he would have gone directly to find Principal Zhao himself.

Thanks for everyone’s support, the results are okay.

However, I have used up all the manuscripts I have in stock, so I will post as much as I can in the next few days, and try to update as quickly as possible while ensuring the quality.

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(End of this chapter)