However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.

However, not all infinite sets have the same cardinality.

However, its impact on the market is yet to be measured, as is consumer attitude toward watching TV programs on personal computer instead of television sets.

However, this is a relatively small number especially when playing with more than four people, so many domino sets are " extended " by introducing ends with greater numbers of spots, which increases the number of unique combinations of ends and thus of pieces.

However, while there are many passages where the Gospel of Barnabas sets out alternative readings to parallel pericopes found in the canonical gospels, none of the references to Muhammad by name occurs in such a synoptic passage ; and in particular, none of the " Muhammad " references in Barnabas corresponds to a " Paraclete " reference in canonical John.

However, the cataclysm sets up an event horizon in time that prevents anyone from entering Gallifrey's relative past or travelling from it to the present or future.

However, in Bush's manuscript draft of " Memex II " of 1959 ( also published in ), Bush says, " Professional societies will no longer print papers ..." and states that individuals will either order sets of papers to come on tape-complete with photographs and diagrams-or download ' facsimiles ' by telephone.

However, if an inaccessible cardinal κ is assumed, then the sets of smaller rank form a model of ZF ( a Grothendieck universe ), and its subsets can be thought of as " classes ".

However, the set existence axioms of NBG are restricted so that they only quantify over sets, rather than over all classes.

However, over the centuries, the age sets grew out-of-alignment with the actual ages of their members, and some time in the 19th century, another age set system was instituted.

However for certain sets of such polynomials it may happen that for only finitely many combinations all polynomial functions take the value zero.

However, many organisms have more than two sets of homologous chromosomes and are called polyploid.

However, in addition to the 12 extruded pentominoes, 6 sets of chiral pairs and 5 pieces make total 29 pieces, resulting 145 cubes, which will not make a 3D box.

However, Pascal also has many data structuring facilities and other abstractions which were not included in the original ALGOL 60, like type definitions, records, pointers, enumerations, and sets.

However, one can consider arbitrary types such as boolean values, categorical variables, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, functions, and processes.

However, with the fall of communism, and following a period when multi-standard TV sets became a commodity, many Eastern European countries decided to switch to PAL.

However, East Germans responded by buying PAL decoders for their SECAM sets.

However, as Benno Werlen remarked, these different perceptions are nothing else than different answers to the same two ( sets of ) questions, which refer to the spatial constitution of society on the one hand, and to the spatial expression of social processes on the other.

However, Soderbergh felt that it was not enough money due to the demands of the project such as the 1960s-era sets and props and the multi-continental settings.

However, the metaphorical view sets a metaphysical ground to the dilemma.

However, the next day a shooting sets off another incident in the same area that leads to 18 fires, 36 arrests, 3 shootings, 2 dozen people injured, and damages totaling 4. 2 million.

However, the general definition remains valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.

However, winter sets in, preventing an immediate battle.

However, the second definition, the intersection of all convex sets containing X is well-defined, and it is a subset of every other convex set Y that contains X, because Y is included among the sets being intersected.

However, the possible absence of a center of symmetry not only moves the hydrogen atom off Af, but also allows the oxygen atoms to become nonequivalent, with Af at Af and Af at Af ( space group Af ), where Af represents the oxygens on one side of the Af layers and Af those on the other side.

However, compared with March 1960 new car sales of 4,441, this March was off 23 per cent.

However, for many acts the " off season " does not mean a period of inactivity, they use time for maintenance and practice.

However, the effects of acid rain can last for generations, as the effects of pH level change can stimulate the continued leaching of undesirable chemicals into otherwise pristine water sources, killing off vulnerable insect and fish species and blocking efforts to restore native life.

However, the arms are the result of an 18th-century restoration, as the original had the arms cut off in order to allow water to flow out.

However, when observing the native bees in the Canterbury province in the South Island, the scientists were astonished to see the bees biting the top off the buds, then pushing with their legs, occasionally popping open the buds to allow the bees to harvest the nectar and pollen, and therefore aid in the pollination of the mistletoe which is in decline in New Zealand.

However, Chad has not recognised the State of Israel since former Chadian President François ( Ngarta ) Tombalbaye broke off relations in September 1972 as an act of solidarity with the Palestinians, and other Arabs under Israeli occupation.

However after falling in love with Peter Barlow, despite doing nothing about it, Carla calls off their wedding.

However, since the contras failed to win widespread popular support or military victories within Nicaragua, since opinion polls indicated that a majority of the U. S. public was not supportive of the contras, since the Reagan administration lost much of its support regarding its contra policy within Congress after disclosure of CIA mining of Nicaraguan ports, and since a report of the Bureau of Intelligence and Research commissioned by the State Department found Reagan's allegations about Soviet influence in Nicaragua " exaggerated ", Congress cut off all funds for the contras in 1985 by the third Boland Amendment.

However his hasty return on August 18 sparked off fierce inter-tribal clashes between the Issa and the Gadabuursi, which in turn caused the Gadabuursi to withdraw from Djibouti politics and did not return to the political scene until after Djibouti's independence.

However, diodes can have more complicated behavior than this simple on – off action.

However, the fact that they can be used " off the shelf ", as well as their amortized cost over many applications and instances, makes them an attractive alternative ( Vs. one-time development ) whenever they meet an application's requirements.

However, Emsworth failed to take off as a seaside resort.

However, these synapses are regained following a period of recovery that includes gradual weaning off of ethanol.

However, a planned referendum on a roadmap towards independence in 2001 was called off following Danish Prime Minister Poul Nyrup Rasmussen saying that Danish money grants would be phased out within four years if there was a ' yes ' vote.

However, it tarnishes quickly in moist air, forming a loosely adhering gadolinium ( III ) oxide ( Gd < sub > 2 </ sub > O < sub > 3 </ sub >), which spalls off, exposing more surface to oxidation.

However, it is as such that she is ultimately treated-rather than being prosecuted in an open trial ( which she might have welcomed ) Annie is discreetly packed off to a private asylum.

However, on May 8, 2010, a sighting of a gray whale was confirmed off the coast of Israel in the Mediterranean Sea, leading some scientists to think they might be repopulating old breeding grounds that have not been used for centuries.

However, due to the quicker growth in the beginning, a few weeks of grow time can be shaved off.

However, there are still minimum weather conditions that must be present in order for the aircraft to take off and land ; these will vary according to the kind of operation, the type of navigation aids available, the location and height of terrain and obstructions in the vicinity of the airport, equipment on the aircraft, and the qualifications of the crew.

However, in June, forces loyal to Constantius captured the city of Aquileia on the north Adriatic coast, an event which threatened to cut Julian off from the rest of his forces, while Constantius's troops marched towards him from the east.

However, he was wrecked on HMS Victoria when it collided with HMS Camperdown ( the flagship of the Commander-in-Chief of the Mediterranean Fleet, Vice-Admiral Sir George Tryon ) off Tripoli on 22 June 1893 ; the Admiral, 21 officers and 350 men drowned.

However, Maloney insisted on repeatedly " shaking off " his younger catcher and throwing the fastball instead of the breaking balls Bench called for.

However, its original purpose was to evade an opponent's floor sweep and flip to the antagonist's exposed side or it may be used as a double aerial kick to an opponent standing off to the side.

However, the kick is intentionally aimed slightly off target in the direction of the kicking foot's toes.