Suppose I have a short exact sequence of Abelian groups 0 -> A ->B ->C ->0, then for any abelian group G I get a short exact sequence 0 -> Hom(C,G) -> Hom(B,G) -> Hom(A,G).
I know that if the original sequence splits, then we get a map Hom(A,G) -> 0. My question is how come we cannot guarantee the existence of this map is the sequence does not split?
Is there any tool that already does this? Where can I find it? Is there a package that can allow me to write this? I'd prefer if it's python, thanks.
Currently confronting myself with the concept of chain complexes and (short) exact sequences.
First things first: the concept of a chain complex appears natural to me. Given two maps f,g such that g°f=0 is not that far off when taken into account that is how kernel and cokernel are defined in the first place. Generalizing this to a sequence of objects A_i and morphisms d_i:A_i→A_{i-1} (taken from a suitable category) such that d_{i-1}°d_i=0 for all i is also a (arguably) reasonable step. From here it is immediate to see im d_i<ker d_{i-1}.
Now, we call such a sequence exact iff im d_i=ker d_{i-1}. Of course, given an inclusion one can always ask "and when are they equal".
Anyways, this does not feel satisfying at all. I have read on a few occasions that the concept of (short) exact sequences is a crucial one (if not the most important) in Homological Algebra. Simply thinking that it arose when asking "and when are they equal" and then realising "oh, that's actually pretty neat" appears quite improbable to me.
Especially when reading about (short) exact sequences in terms of an introduction to Homological Algebra, I have got the feeling some kind of motivation is missing. Chain complexes and exactness are introduced right away but I do not get the latter one (which is unsatisfying, given the apparent importance of exactness).
So, could you please explain to me why to care about (short) exact sequences at all?
Thanks in advance!
New to this sub and I am sorry if there are already lots of COVID and vaccine questions here. I understand the classic dogma of DNA to RNA to Proteins and Enzymes and understand for a virus to infect you, it inserts its DNA sequence into your genome so that it can start producing viral particles. My question is if the mRNA sequence used in the vaccine is the exact same as what would be produced if you are infected with COVID? If so, would that mean that any and every symptom you could get from the vaccine would also happen if you got COVID? Would the lipids attached to the vaccine mRNA sequence make a huge difference (besides slowing how fast your body breaks it down)? And are there any other ingredients in the vaccine besides saline solution? Would those ingredients cause any sort of effect besides the intended immune response? How experimental is mRNA vaccines anyways?
I am under the impression that it is no big deal, that plenty of research has gone into this, and that expectations of effects down the line are outlandish and based in misinformation about the vaccine changing your DNA, and that vaccine side effects usually come on quick, like an allergic reaction within minutes, or an autoimmune attack within weeks (adenovirus vectors in Astrazeneca or flushots). But I also understand the body is very complex, and small changes can compound.
Does anyone know what Joji's complete DNA sequence looks like? I wanna know so I can replicate it and clone him in a lab and make him my boyfriend. god I want joji to be my boyfriend so bad pls let him be my bf hngrshrbrhdjfhjjdk joji bf joji bf joji bf my mental health is rapidly declining joji bf
Hatcher states that relative cohomology is conceptually simpler than relative homology because the cochain group C^n (X,A;G) can be viewed as the subgroup of C^n (X;G) whose elements are zero on Cn(A), so the short exact sequence of cochain groups splits. However, it appears to me that the analogous sequence for homology should also split, with Cn(X,A;G) embedding as the subgroup of Cn(X;G) generated by the singular simplices not contained in A. (In particular, this would give a much shorter proof that the dual sequence is in fact exact than the one Hatcher gives.) Why does this not work?
I don’t just mean in your life (although that is crazy too); I mean the universe as a whole. First the universe and matter just simply existed, that in itself is insane. All this matter came together and expanded to create the universe including our galaxy. In our galaxy our sun happened to form and so did our planet in the EXACT location and conditions to make life possible (oxygen, water, temperature, gravity, etc.). Somehow life just happened to emerge and organisms composed of cooperating cells just happened to form.These species survived long enough to evolve to fungi to plants to animals.
Through evolution this eventually led to the formation of mammals and then primates then humans. These humans were able to use materials they found in their environment and compose them into devices and tools. They survived cataclysmic events such as the ice age, ferocious predators and plagues. We were able to capture and tame entire other species to work for us and be our companions (wtf?).
We made vehicles to quickly travel through and over water, land, air and even space (we saw a big rock in the sky and were like “yo, lets go there”, AND WE DID IT). We were able to harness electricity and computers (this all happened in ~150 years). We are able to capture images and sound indefinitely through recording. We were able to make entire networks that connect people around the world accessed through small devices we carry around in our pockets, from material we just found and figured out how to mold. We formed society (also an insane concept) to cater to our comfort and desires that were originally just in place to ensure our survival (heating and air conditioning, restaurants, bars (social areas)).
I just believe that it is crazy that all these events happened and the result is where we are right now. There are so many things we take for granted and accept as “normal” whereas in reality they are absolutely insane. The universe is a crazy, beautiful place.
I've been an ape since Jan 27th when I created this account. My cake day is coming up. I'm not a shill or trying to spread FUD, I just want to better understand the mechanism that forces shorts to close their positions when it seems they can kick the can for years. I want this wrinkle.
Is it the DTCC that would force shorts/naked shorts to close their positions? Are there other lending entities that would force closing?
My smoothe brain wants to understand.
How does this work?
Thank you from a fellow ape.
Now eat your goddamn crayons like Momma ape always told you to:
🖍🖍🖍🖍🖍🖍🖍🖍🖍🖍🖍🖍🖍
So very frequently when I watch people making YouTube videos judging routines, they'll say "dance sequence not valid (not 8 seconds long)" etc.
Is there a penalty for this? How does it work?
Also, what is a dance sequence really defined as? How do they know when it starts and ends to the millisecond? Because it seems like the gymnast is still doing Apparatus Difficulties during the dance sequence...no? Like, it's not like they're literally just dancing without doing anything with the apparatus, lol.
Also, what are other composition requirements? I think there's a max. and min. number of risks...right? Or is that a past COP?
V clueless here :-)
The bit with the guy's eye shield shattered? Pretty sure I watched the short in question years ago on YouTube, but for the life of me I cannot recall the name.
I know we all took it with a massive grain of salt… but I mean come on. I hope everyone listened to the little voice in their head telling them that JP is a total shit nugget and they didn’t lose a ton on options, but I know with the info of tomorrow option chain that is unlikely. JP can dine on a bag of dicks tonight.
tears streaming down my face thinking: “Why does this exist?” I reread it every year just to torture myself but I love the way its written, and would recommend this to anyone, with a trigger warning of course.
It wasn't outright bad, it was just bland and unsatisfying.
In case it wasn't obvious, spoiler alert.
It completely whiffs on all the big plot points
-
Conflicts within Seowoo's family resolves with the father throwing something at Seowoo shown in a single panel, and she left home and that's it?
-
Yi-hwa's issue with her mother, a few short panels in the hospital and that was it?
-
Throughout the chapters Hayoung was afraid of people judging them for being in a relationship, and... nothing ended up happening?
-
Director Baek Sang and Ga-Eun, it just ended in the most unsatisfying way possible, what the heck?
-
Two main characters lack personality and charm. Honestly Ga-Eun is way more interesting than anyone else in the cast, even Yi-Hwa is more interesting.
-
Speaking of Ga-Eun, she's criminally underutilized, we saw one instance of her swearing at a customer, and that was it. There's way too much unexplored potential here.
-
I just realized I much prefer if this webtoon was about Ga-Eun instead lol.
So yeah, in conclusion, this webtoon reads like a manga series that got killed by the publisher and is forced to end quickly with no budget to properly tie up loose ends.
My initial thoughts are either just give him the level and don't worry about it or try to run a mini session to explain his character's absence. Would love to hear some other thoughts.
Edit: Am I really catching downvotes for asking for advice?
Apparently people are thinking I was going to not give him the level or somehow punish him. If you read, I'm asking how I should go about leveling him. I'm not considering holding him back.
Edit 2: Surprised by the huge response on this post. Thanks for everyone's input, I still think lots of people got the wrong idea about what I was asking but that's likely my fault for being unclear. For the most part the advice given has reinforced what I was leaning towards. What I ended up doing was messaging the party groupchat with
"Everyone gets a level btw Including Aris who, though he missed the fights, was fighting for his goddamned life."
For those that asked, the missing character was not in game with the rest of us. He has a genie bottle he can go into and we quickly decided that the bottle had been misplaced at the camp the night before. I don't like playing PCs for people because choices can be made that accidentally go counter to the player's intentions.
If I'm able to do a quick one on one I'll figure out what he was up to while the rest of the party was questing but if not he'll just rejoin the party next time and I'm sure he'll be able to do a bit of RP to smooth the gap. No big deal.
In a bit of meta commentary, I think a number of the commenters we're really quick to act like this question was absurd or out of line or even offensive to your sense of justice. Even if I had been considering holding him back a level I think that sort of reaction to an honest inquiry is a bit much. I recommend you folks be a little more charitable in your interpretations in the future or this sub will start to look like the RPG equivalent of r/RelationshipAdvice.
Been an investor in crypto since 2016, and we have see the same pattern over and over again since crookstreet got into the cryptocurrency ecosystem by the masses at the end of 2017. Wave of new users will join a subreddit/telegram channel, show excitement with dates, share bunch of positive memes, boost up morale to cloud nine then at the first opportunity to attack when there are project tumbles or delays, they flood the feed with negative comments and create low morale posts to keep out the real community members and potential new retail investors!
They infiltrate --> Bring positive noise --> Create FUD --> Continue to drive the energy into the ground to divide the community.
Just do a quick search online. The same MSM that has tried to spread FUD with GME is doing the same with LRC.
Same Shill Tactics by News Outlets that are Owned by Hedge Funds
Another recent examples are with the subreddits Superstonk and GMEJungle started up, we saw the same patterns of shillbots, asking specific date releases and the strategy, so they can short the stock to match their negative propaganda by MSM.
Crookstreet wants LRC for themselves because this will change the game entirely. Their unnecessary existence is threatened to the core.
Cancel the noise like you have always done these past 4+ years, Loopring!
LRC team you guys are doing great! We are behind you every step along the way!
Like the saying goes, if you don't have some haters along the way of the journey then you are not doing it right!
You guys are heading in the right direction! Keep going!
Please read this first before commenting
So the original question is “What comes next?” —-> “⬜️,⬜️⬜️,⬜️⬜️⬜️,__________?”
It was in one of my tests for geometry and I answered ⬜️, but the actual answer was ⬜️⬜️⬜️⬜️. This was around 3 years ago I feel like I lack logic
Pretty much exactly what the title says. I know Apes are thinking "well they will just shorts it back to $150 once it reaches $350, and it will be the endgame all over again".
Putting on my tin foul cap but I believe they are deliberately creating this repetitive cycle of running it to 350 and crashing it back to 150 to make Apes say "well fuck it if it's going to keep doing this, I might as well day trade".
DFV never sold, he could have had legendary realized gains but the fucking legend never day traded GME and QUADRUPLED down, fucking legend.
Me personally, I will not let shorts tempt me to get off the rocket to make puny gains just to get left behind once the rocket takes off.
Not financial advise, just sharing my thoughts and my personal strategy.
Edit:
Wow lots of people calling me a shill, saying FUD, telling me to fuck off so here's an update to those saying that "Noone thinks like that you are a shill implanting FUD".
If I'm being honest, I've been poor my whole life so when I see a trend showing I could have made thousands of dollars by day trading it looks tempting because the poor side of me is telling me "oh look at all the money you could have made".
But I'm saying despite feeling like that, I've come to realize how stupid it would be to miss the rocket launch into retirement by pinching profits.
I have had Apes reach out to me and tell me they felt the same way and that the post helped them also realize how dumb it would be.
Just being honest about how I feel and trying to help other Apes realize the same.
Is that fair? Or should I still fuck off?
I’m wondering that when the definition of a sequence of abelian group is given by:
…-> C_n+1 -> C_n -> C_n-1 ->…
Why is the definition of the homology groups for short exact sequence given as
0- >H_n(A) -> H_n(B) -> H_n(C) -> …
For short exact sequence being
0-> A_* -> B_* -> C_* ->0
And not
0- >H_n+1(A) -> H_n(B) -> H_n-1(C) -> …
Is it because that it’s already implied in
0-> A_* -> B_* -> C_* ->0
That
0-> A_n+1 -> B_n -> C_n-1 ->0
If then how are all the homologies H_n along the chain have the same n's ???
