Instead of focusing merely on the individual objects ( e. g., groups ) possessing a given structure, category theory emphasizes the morphisms – the structure-preserving mappings – between these objects ; by studying these morphisms, we are able to learn more about the structure of the objects.

Instead of just studying Halakha, Louis Ginzberg wrote responsa, formal responses to questions of Jewish law.

Instead of studying nature directly, younger artists began studying Hellenistic sculptures and paintings of masters past.

Instead of groups, groupoids, the mathematical generalization of groups in category theory, is the appropriate tool for studying quasicrystals.

Instead, new and borrowed verbs and adjectives are conjugated periphrastically as verbal noun + suru ( e. g. benkyō suru ' do studying = study ') and adjectival noun + na.

Instead, he used his grandfather's legacy and a small borrowed sum to spend the next two years studying the educational systems of the Old World in Europe.

Instead, functional rather than geographical intelligence requirements came to the fore such as counter-proliferation ( via the agency's Production and Targeting, Counter-Proliferation Section ) which had been a sphere of activity since the discovery of Pakistani physics students studying nuclear-weapons related subjects in 1974 ; counter-terrorism ( via two joint sections run in collaboration with the Security Service, one for Irish republicanism and one for international terrorism ); counter-narcotics and serious crime ( originally set up under the Western Hemisphere Controllerate in 1989 ); and a ' global issues ' section looking at matters such as the environment and other public welfare issues.

Instead of studying hard or conducting military affairs, he was always in the presence of court officials in order to gain their support.

Instead, Hooper decided on a career in law, studying under James Otis, a popular attorney in Boston who was regarded as a radical.

Instead of studying the bass playing of someone like John Entwistle, which would have given me a foundation of how to play.

Instead of being only a worrisome problem, renormalization has become an important theoretical tool for studying the behavior of field theories in different regimes.

Instead of having to pay each year while studying, students are to be loaned the funds by the government and repayments will be made out of income once the graduate is earning more than £ 15000 per year.

Instead learner interest guides things, with students studying what they want to study.

Instead, Lane joined his brother Richard in London, studying engraving with him.

Instead of studying martial arts, like his fellow bodyguards, Ling Ling Fat makes unusual inventions, such as cannons fired from the mouth, helicopter blades, and magnets.

Instead Neptune was predicted using Newton's law of universal gravitation.

Instead of just establishing it as a military prison, he provided for a civil administration, with courts of law.

Instead, it presumably refers to the practice of setting law books and citing legal precedents in blackletter type, a tradition that survived long after the switch to roman and italic text for other printed works.

Instead, murder is treated as a civil crime and is covered by the law of retaliation, whereby the relatives of the victim decide whether the offender is punished with death by the authorities or made to pay diyah as compensation.

Instead, it maintained a system of taxation on the production that took place in the territories that they controlled, in exchange for protecting the growers and establishing law and order in these regions by implementing its own rules and regulations.

Instead, the law compelled the authorities to sell gold bullion on demand at a fixed price, but only in the form of bars containing approximately four hundred troy ounces of fine gold.

Instead the Emperors reserved the implementation of the bishops of their proprietary church for themselves, defying the fact that according to canon law they were part of the transnational Catholic Church.

Instead, international law has been used with respect to the specific categories of weapons within WMD, and not to WMD as a whole.

Instead of executing Mulan as the law requires, Li Shang decides to spare her life by leaving her on the mountain as the rest of the army departs for the Imperial City to report the news of the Huns ' demise.

Instead of executing Mulan as the law requires, Li Shang decides to spare her life, leaving her on the mountain as the rest of the army departs for the Imperial City to report the news of the Huns ' demise.

Instead, appeals courts review decisions of trial courts for errors of law.

Instead of considering Leibniz's law as an axiom, it can also be taken as the definition of equality.

Instead, law enforcement is the responsibility of the county Sheriff, who is a constitutional officer elected every four years.

Instead, opponents denounced the law as a concession to the slave power of the South.

Instead, it contended that the law separated the two races as a matter of public policy.

Instead, the overarching story of all five seasons of the series pitted Angel as the central player in a battle between the " good " Powers That Be and the " evil " law firm Wolfram & Hart and his possible role in a prophesied apocalypse.

Instead, the court held that the right to the assistance of counsel was a fundamental right, essential for a fair trial, thereby emphasizing the procedural safeguards needed for due process of law.

Instead, the Apalachin Meeting turned into a terrible fiasco when law enforcement raided the meeting.

Instead, they were proponents of natural law, created by the King's authority, not by any individual judge.

Instead, he has worked towards establishing reliable political customs when transitioning one government administration to another, emphasizing constitutional law and protocol, and representing the Spanish State domestically and internationally, all the while maintaining a professionally non-partisan yet independent monarchy.

Instead of transparently enforcing the rule of law and being subject to public scrutiny as ordinary police agencies do, secret police organizations are specifically intended to operate beyond and above the law in order to suppress political dissent through clandestine acts of terror and intimidation ( such as kidnapping, coercive interrogation, torture, internal exile, forced disappearance, and assassination ) targeted against political enemies of the ruling authority.

Instead, Stevens was offered a job with the Fairbanks, Alaska, law firm of Emil Usibelli's Alaska attorney, Charles Clasby, whose firm – Collins and Clasby – had just lost one of its attorneys.

Instead of giving themselves spontaneously to the orgiastic release that jazz can give them, they undergo psychoanalysis or flirt with mysticism or turn to prostitutes for satisfaction.

Instead of radiators you'll have cooling-heating units, each with its own thermostat.

Instead, he constantly became lost in parts and components of them, confused some of their details with those of neighboring objects, and so on, unless he allowed time to `` trace '' the object in question through minute movements of the head and hands and in this way to discover its contours.

Instead of isolating the literal flatness by specifying and circumscribing it, the pasted paper or cloth releases and spreads it, and the artist seems to have nothing left but this undepicted flatness with which to finish as well as start his picture.

Instead he brought with him the names of some people he had never met and of whom the medium knew nothing.

Instead, the audience can sit back at ease and, from the perspective of an enlightened time which no longer believes in such things, enjoy the dead seriousness with which the characters in the play take the witches and devils which are under discussion.

Instead of linking the nine numbers of this diagram with the traditional Nine Provinces, as was usually done, this equated the odd, Yang numbers with mountains ( firm and resistant, hence Yang ) and the even numbers with rivers ( sinuous and yielding, hence Yin ) ; ;

Instead -- and not just to prove my objectivity -- I hasten to report that it's a highly amusing film which probably does a fairly accurate job of reporting on the Easter vacation shenanigans of collegians down in Fort Lauderdale, and that it seems to come to grips quite honestly with the moral problem that most commonly vexes youngsters in this age group -- that is to say, sex.

Instead the cartoons seem to deal with foibles.

Instead of having a pulp cavity, each tooth has a cluster of thin, upright, parallel tubes of vasodentin ( a modified form of dentine ), with individual pulp canals, held together by cementum.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Instead, the irrigated agriculture project was headed for completion with apparently no prospects for extension beyond 2011.

Instead, Rufinus attempted to negotiate with Alaric in person, which only aroused suspicions in Constantinople that Rufinius was in league with the Goths.

Instead, that night ( July 17 / 18 ), Alexios III hid in the palace, and finally, with one of his daughters, Eirene, and such treasures ( 1, 000 pounds of gold ) as he could collect, got into a boat and escaped to Debeltos in Thrace, leaving his wife and his other daughters behind.

Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of the operating system.

Instead of using Vermin's tired characters, Abner inventively peopled the strip with hillbillies.

Since the 2002 edition, the Apostles ' Creed is included in the Roman Missal with the indication, " Instead of the Niceno-Constantinopolitan Creed, especially during Lent and Easter time, the baptismal Symbol of the Roman Church, known as the Apostles ’ Creed, may be used.

Instead of reviewing music videos, they reviewed ( custom-made ) pages from other Marvel Comics — in one with Ghost Rider, Beavis tries to avoid using the word " fire " to describe the character's fiery skull.

Instead, space itself expands with time everywhere and increases the physical distance between two comoving points.

Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.

Instead, the Hebrew name Ahasuerus accords with an inscription of the time that notes that Artaxerxes II was named also Arshu, understood as a shortening of Achshiyarshu the Babylonian rendering of the Persian Khshayarsha ( Xerxes ), through which the Hebrew Achashverosh ( Ahasuerus ) is derived.