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Page "Category theory" ¶ 12
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Some Related Sentences

Abstracting and again
Abstracting yet again, constructions are often " naturally related "a vague notion, at first sight.

Abstracting and for
" Abstracting the future: The Search for Musical Constructs " Computer Music Journal 20 ( 3 ): 24-27.
Abstracting and indexing services for various academic disciplines are aimed at compiling a body of literature for that particular subject.

Abstracting and called
Subsequently, for-profit firms ( called Abstracting and indexing services ) emerged to index the fast-growing literature in every field of knowledge.

Abstracting and .
Abstracting from relations instead of functions yields allegories instead of categories.

again and category
In a 6 optional meet, the divers will yet again perform one dive from each category, but this time they will perform a 6th optional from the category of their choosing, which is worth its actual DD from the DD sheet.
In any category, the composition of any two endomorphisms of X is again an endomorphism of X.
) The composition of two such homomorphisms is again a homomorphism, and the class of all Lie groups, together with these morphisms, forms a category.
The country partly rebuilt its economy during the 1990s, but was hit hard by Hurricane Mitch at the end of October 1998, almost exactly a decade after the similarly destructive Hurricane Joan and again in 2007 it was hit by Hurricane Felix a category 5 hurricane.
They won a Grammy Award in 1999 in the Best Polka Album category for their album Polkasonic, and again in 2005 for their album Let's Kiss.
This forms a category since for any functor F there is an identity natural transformation ( which assigns to every object X the identity morphism on F ( X )) and the composition of two natural transformations ( the " vertical composition " above ) is again a natural transformation.
According to chairman of the club Eric Gudde the placing in the more favourable category came earlier than anticipated, he also congratulated the fans and promised to maintain the same policy until Feyenoord was completely healthy again and will never fall back into the first category.
The 32nd Academy Awards saw the category again be split into two for recognition of both Black and white and color film.
An example of a non-abelian, pre-abelian category is, once again, the category of topological abelian groups.
Site Selection again recognized the efforts of the Opelika Economic Development Department in its Top Groups 2005 list in the Honorable Mention category.
What is new here is that the above expresses the requirement for associativity without any explicit reference to individual morphisms in the enriched category C — again, these diagrams are for morphisms in hom-category M, and not in C — thus making the concept of associativity of composition meaningful in the general case where the hom-objects C ( a, b ) are abstract, and C itself need not even have any notion of individual morphism.
Once again Campanella engages in an explicit polemic with Aristotle, who had excluded artisans, peasants and those involved in manual labor from the category of full citizenship and from the highest levels of virtue.
# It follows from the previous example that the opposite of any concretizable category C is again concretizable, since if U is a faithful functor C → Set then C < sup > op </ sup > may be equipped with the composite C < sup > op </ sup > → Set < sup > op </ sup > → Set.
" The program received the award again two years later in the same category, the committee concluding that Huntley and Brinkley had " dominated the news division of television so completely in the past year that it would be unthinkable to present a Peabody Award in that category to anybody else.
Yet again, in 1974 the term multi-infarct dementia was coined and all vascular dementia was grouped into one category.
In the 1974 / 75 season, with Eugenio Montes Cabeza as president and Roque Olsen as trainer, the club obtained again the promotion to First Division and settled in this category with great stability.
In 2005 and again in 2009, Vieira won a Daytime Emmy Award as Outstanding Game Show Host for her role on Millionaire, being the second woman to ever win an Emmy in this category ( after Betty White for Just Men!
In 2012, both categories were once again combined into the new Best Children's Album category.
The category was reinstated for 1967 through 1969, before lapsing again ; after returning in 1973 it has remained to date.
Slightly more generally: if ( X, O < sub > X </ sub >) is a ringed space, then the category of all sheaves of O < sub > X </ sub >- modules is an abelian category with enough injectives, and we can again construct sheaf cohomology as the right derived functors of the global section functor.

again and is
In addition to the authentication and acknowledgment procedures which precede and follow the sending of the go messages, again in special codes, each message also contains an `` internal authenticator '', another specific signal to convince the recipient that he is getting the real thing.
`` As my wife puts it '', he said, again with a twinkle in his eyes, `` all you know is your music.
The hero, who is himself, is represented as a pilgrim in the storied lands of the East, a sort of Faustus type, who, to quote from Professor Book again, `` even in the pleasure gardens of Sardanapalus can not cease from his painful search after the meaning of life.
Years ago this was true, but with the replacement of wires or runners by radio and radar ( and perhaps television ), these restrictions have disappeared and now again too much is heard.
Only when that term is ended and he is a private citizen again can he be permitted the freedom and the courage to discount the dangers of his death.
The American Medical Association is once again grinding out its tear-soaked propaganda based upon the high cost of the Veterans Administration medical program to the American taxpayer.
He says that if he were to express to you, once again, his own profound determination to go to the Mainland, and his faith that that return is feasible, he would merely sound redundant.
and, though he repeated, over and over again, the spectacular figures of industrial and agricultural production in 1980, the `` ordinary '' people in Russia are still a little uncertain as to how `` communism '' is really going to work in practice, especially in respect of food.
He could no longer build anything, whether a private residence in his Pennsylvania county or a church in Brazil, without it being obvious that he had done it, and while here and there he was taken to task for again developing the same airy technique, they were such fanciful and sometimes even playful buildings that the public felt assured by its sense of recognition after a time, a quality of authentic uniqueness about them, which, once established by an artist as his private vision, is no longer disputable as to its other values.
It was recognized years ago that the transition from daytime to nighttime propagation conditions, and vice versa, is not an instantaneous process, but takes place over periods of time from roughly 2 hours before sunset until about 2 hours after sunset, and again from roughly 2 hours before sunrise until some 2 hours after sunrise.
When the front knee is straight and locked, allow it to bend again until you feel the bar come lightly into contact with the sides of the Power Stands.
By this scheme, pulling one signal to clear locks all the other switch and signal levers in safe positions until the first signal is again restored to normal.
He is going sound again now, and looks good.
Before it cycles on again, humidity can build up and make you uncomfortable even though the temperature is still low.
What I have observed time and time again is a process of integration, integration that begins as abstract design and gradually takes on recognizable form ; ;
And how very often a water plane is featured in his landscapes, and how appropriate that he should appear in American Artist again, in his natal month of March!!
there is a struggle there, in which, if he falls, it is easy for him to rise again, there is freedom of utterance there, which draws after it no irreparable consequences on society.
If you would feel happier with full collision insurance, there is a small additional charge, again varying from country to country and depending on the term of such insurance.
and that the maximum of the radio emission came about 3-1/2 days after Full Moon, which is again in contrast to the infrared emission, which reaches its maximum at Full Moon.
The argument against this last approach is comparable to that which rejects stories about hoop snakes, about snakes that break themselves into many pieces and join up again, or even of ghosts that chase people out of graveyards ; ;
Here again, in the written language it is possible to help the reader get his stresses right by using underlining or italics, but much of the time there is simply reliance on his understanding in the light of context.

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