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The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.
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snake and lemma
Abelian categories are very stable categories, for example they are regular and they satisfy the snake lemma.
The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.
To see where the snake lemma gets its name, expand the diagram above as follows:
and then note that the exact sequence that is the conclusion of the lemma can be drawn on this expanded diagram in the reversed " S " shape of a slithering snake.
This follows from the naturality of the sequence produced by the snake lemma.
is a commutative diagram with exact rows, then the snake lemma can be applied twice, to the " front " and to the " back ", yielding two long exact sequences ; these are related by a commutative diagram of the form
* The proof of the snake lemma is being taught by Jill Clayburgh at the very beginning of the 1980 film It's My Turn.
Examples of proofs by diagram chasing include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma.
All maps in this long exact sequence are induced by the maps between the chain complexes, except for the maps H < sub > n </ sub >( C ) → H < sub > n-1 </ sub >( A ) The latter are called connecting homomorphisms and are provided by the snake lemma.
The snake lemma can be applied to homology in numerous ways that aid in calculating homology groups, such as the theories of relative homology and Mayer-Vietoris sequences.
The maps δ < sup > n </ sup > are called the " connecting homomorphisms " and can be obtained from the snake lemma.
The above-mentioned property of turning short exact sequences into long exact sequences is a consequence of the snake lemma.
Both of these naturalities follow from the naturality of the sequence provided by the snake lemma.
The nine lemma can be proved by direct diagram chasing, or by applying the snake lemma ( to the two bottom rows in the first case, and to the two top rows in the second case ).
The following year he played a student who raised objections during Jill Clayburgh's proof of the snake lemma in the film It's My Turn.
An application of the snake lemma then yields a long exact sequence
snake and is
The following information on snakes varying greatly in size ( but all with less than a 10-foot maximum ) shows, when considered with the foregoing, that there is probably no correlation between the length of a snake and the time required for it to mature.
every snake hide is noticeably longer than its carcass and intentional stretching presents no difficulty to the unscrupulous explorer.
The medical device pirate of today, of course, is a far more sophisticated operator than his predecessor of yesteryear -- the gallus-snapping hawker of snake oil and other patent medicines.
The western terrestrial garter snake ( Thamnophis elegans ) in California is largely aquatic and depends heavily on two species of frog that are diminishing in numbers, the Yosemite toad ( Bufo canorus ) and the mountain yellow-legged frog ( Rana muscosa ), putting the snake's future at risk.
An anaconda is a large, nonvenomous snake found in tropical South America.
* The giant anaconda is a mythical snake of enormous proportions said to be found in South America.
However, this name is used to refer to the brown vine snake, Ahaetulla pulverulenta, a slender, arboreal species that grows to five feet ( 152 cm ) at most and feeds only on small vertebrates.
The account, which explains how the snake crushes and devours tigers, is full of popular misconceptions, but was much read at the time, and so gave rise to the myth of the anaconda of Ceylon.
Antlia is bordered by Hydra the sea snake, Pyxis the compass, Vela the sails, and Centaurus the centaur.
Two is " snake eyes ," because the two ones that comprise it look like a pair of small, beady eyes.
Air is represented in the Aztec religion by a snake to the Scythians, a yoke to the Hindus and for Greeks as a sword and in Christian iconography as mankind.
The four species include the leopard snake ( locally known as Ochendra ), the Balkan whip snake ( locally called Dendrogallia ), the dice snake ( called Nerofido in Greek ), and the only venomous snake is the nocturnal cat snake which has evolved to deliver its venom in to geckos and small lizards and is not dangerous to humans.
This snake feeds on the larvae, eggs and pupae of ants and termites, and is about the size of a large earthworm.
His image is a double-helix snake, or the Caduceus, very similar to the Rod of Asclepius used to symbolize medicine.
In the Italian Ambrosio companies film La mala planta ( The Evil Plant ), directed by Mario Caserini, which involves a case of poisoning, there is an Insert shot of a snake slithering over the ‘ Evil Plant ’.
He is not descriptive, so animals including an elephant, monkeys, a seal, a snake, a kangaroo & joey, and turtles are brought to Jon ’ s house for the reward.
snake and tool
* Nicknamed the " snake cam ", it is an essential tool in the Tom Clancy video game Rainbow Six Vegas and the entire Splinter Cell series.
Six months later, Greg has been accepted into Quantico to be an FBI agent, the plant has been reopened as a bar / bike shop where the snake is used as a sales tool, and John finds out that he and Kristin are soon to be parents.
The study found, however, that this toxic effect is simply a tool the snake can choose to employ from an accessory venom gland it has.
:* Bore snake, a tool to clean the barrel of a firearm
* Bore snake, a gun cleaning tool
snake and used
The name was first used in the English language in 1768 by R. Edwin in a colorful description of a large snake found in Ceylon ( now Sri Lanka ), most likely a reticulated python, Python reticulatus.
In 2011 the Djedi Project team used a Micro snake camera ( that can see around corners ) to penetrate the first door of the northern shaft, and view all the sides of the small chamber behind it.
This blood was swallowed by a washer woman, who gave birth to Chen Jinggu ( 陈靖姑 ) or Lady Linshui ( 临水夫人 ); the hair was turned into a female white snake and sexually used men and killed rival women.
One of the most common hieroglyphs, snake, was used in Egyptian writing to stand for a sound like the English ⟨ J ⟩, because the Egyptian word for " snake " was djet.
It is speculated that Semitic people working in Egypt adapted hieroglyphics to create the first alphabet, and that they used the same snake symbol to represent N, because their word for " snake " may have begun with that sound.
The guts of " Nari or Narfi " are then used to tie Loki to three stones, after which the guts turn to iron, and Skaði places a snake above Loki.
As a part of Chinese medicine, scorpion wine and snake wine are used as analgesic and antidote.
The phrase snake oil is a derogatory term used to describe quackery, the promotion of fraudulent or unproven medical practices.
The scientists used mass spectrometry to show that the mixture of proteins present in the venom was as complex as the proteins found in snake venom.
The image of Garuda is often used as the charm or amulet to protect the bearer from snake attack and its poison, since the king of birds is an implacable enemy and " devourer of serpent ".
This copper snake according to the Biblical text is wrapped around a pole and used for healing.
Another version is used in alchemy whereas the snake is crucified, known as Nicolas Flamel's caduceus.
It also is used to break up kidney stones and gall stones, and was reportedly used as an antidote for both snake and scorpion venom.
Some scholars have noted that a myth arose that the first legendary Emperor of China, Huangdi ( 黃帝, Yellow Emperor ) used a snake for his coat of arms.
In honor of Asclepius, a particular type of non-venomous snake was often used in healing rituals, and these snakes — the Aesculapian Snakes — crawled around freely on the floor in dormitories where the sick and injured slept.
snake ) was used, and thousands of snakes came pouring down from the skies on unsuspecting enemies.
Pecos used a rattlesnake named Shake as a lasso and another snake as a little whip.
A bright yellow snake symbol is used to mark the path
Currently, some snake venom has been used to create anti-coagulants that work to treat stroke victims and heart attack cases.
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