Because of this example, for any preadditive category C, the category Add ( C, Ab ) is sometimes called the " category of left modules over C " and Add ( C < sup > op </ sup >, Ab ) is the category of right modules over C.

Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired ( as is often the case in category theory ).

Because of its applicability in diverse fields of mathematics, mathematicians including Saunders Mac Lane have proposed category theory as a foundational system for mathematics, independent of set theory.

Because of their shared histories and the similarities between the pronunciation, vocabulary and accent of American English and Canadian English, the two spoken languages are often grouped together under a single category.

Because each bike offers virtually identical performance, and because they are relatively cheap to buy and race, it is a popular introductory racing category, particularly in Australia.

*' Because the traits distinguishing metals and nonmetals are qualitative in nature, some elements do not fall unambiguously in either category.

Because of concerns over pilot exhaustion, this record category has been discontinued.

Because the area is a haven for artists, the festival honors them with a special " artist category ", in addition to the documentary, feature and short film categories.

" Because " Simpsons Roasting on an Open Fire " was considered a separate special, The Simpsons was nominated twice in the Animated Program category.

Because they adopt so many musical styles it is hard to place Bela Fleck and the Flecktones into a single musical category and just as their music is diverse, so is their audience.

Because of controversy, most science fiction films will fall into the dystopian film category rather than the Utopian category.

Because the male and female plumages of the Mandarin Duck are so unalike, yuan-yang is frequently used colloquially in Cantonese to mean an " odd couple " or " unlikely pair " – a mixture of two different types of same category.

Because of the high volume of passenger traffic, category X airports are considered vulnerable targets for terrorism.

Because of the overlap of spiritual crisis and mental health problems, Transpersonal Psychologists made a proposal for a new diagnostic category entitled " Psychoreligious or Psychospiritual Problem " at the beginning of the 1990s.

Because of this example, the category Funct ( C < sup > op </ sup >, Set ) is sometimes called the " category of presheaves of sets on C " even for general categories C not arising from a topological space.

Because of this dry season month, the city ’ s climate falls under the tropical monsoon climate category instead of the tropical rainforest climate category.

Because North Korea has been denying the existence of abductees and POWs on its territory, since November 2000, the South Korean government has been trying to resolve the issue through a more realistic approach of including the abductees and POWs in the category of separated families.

Because the majority of enzymes fall within this category, the term is used primarily to differentiate a specific enzyme from an exoenzyme.

Because they are `` minority '' exercises and have but a limited appeal they soon find themselves in the limbo of the forgotten.

Because of this, it would appear inevitable that an increasing percentage of strategic missiles will seek self-protection in mobility -- at least until missile defenses are perfected which have an exceedingly high kill probability.

Because individual classes of foods differ in their requirements for preservation, a number of methods have been developed over the years involving one or a combination of procedures such as dehydration, fermentation, salting, chemical treatment, canning, refrigeration, and freezing.

Because they have kept the faith of their medieval fathers, English Catholics have always strongly resented the charge of being `` un-English ''.

Because if you can't then nobody else can either, nobody else can have him.

`` Because maybe I won't have to wear it always.

Because I liked this sad person so much, I said, `` Will you have a drink with me ''??

Because anthropology developed from so many different enterprises ( see History of Anthropology ), including but not limited to fossil-hunting, exploring, documentary film-making, paleontology, primatology, antiquity dealings and curatorship, philology, etymology, genetics, regional analysis, ethnology, history, philosophy, and religious studies, it is difficult to characterize the entire field in a brief article, although attempts to write histories of the entire field have been made.

Because of the holistic nature of anthropological research, all branches of anthropology have widespread practical application in diverse fields.

Because of the ocean's great capacity to store and release heat, maritime climates are more moderate and have less extreme seasonal variations than inland climates.

Because some have a prevision of the glory to come and others foretaste their suffering, the state of waiting is called " Particular Judgment ".

Because the beaks of giant squids have been found embedded within lumps of ambergris, scientists have theorised that the substance is produced by the whale's gastrointestinal tract to ease the passage of hard, sharp objects that the whale might have eaten.

Because Ambrosius and Vortigern are shown in the Historia Brittonum as being in conflict, some historians have suspected that this preserves a historical core of the existence of two parties in opposition to one another, one headed by Ambrosius and the other by Vortigern.

Because of this, its main stars have no particular pattern and it is devoid of bright deep-sky objects.

Because the technique has allegedly been used to improve breathing and stamina in general, advocates also claim that athletes, people with asthma, tuberculosis, and panic attacks have also found improvements.

In fact, Fitzmyer believes that the preface of Luke should only be “ the starting point in the discussion of the aim of Luke-Acts .” Because the author ’ s intended purpose for the Book of Acts is not that straightforward, scholars have put forth four main claims to address this.

Because field artillery mostly uses indirect fire the guns have to be part of a system that enables them to attack targets invisible to them in accordance with the combined arms plan.

Because these users have different needs, the presentation of financial accounts is very structured and subject to many more rules than management accounting.

Because of this, correct imports of DXF files have been difficult.

Because of these accidents, the various aviation authorities around the world have created set rules and guidance for those running and participating in air displays.

Because of this risk, patients prescribed clozapine may need to have regular blood checks to catch the condition early if it does occur, so the patient is in no danger.

Because individuals with albinism have skin that entirely lacks the dark pigment melanin, which helps protect the skin from the sun's ultraviolet radiation, their skin can burn more easily from overexposure.

Because there is no external pressure for the gas to expand against, the work done by or on the system is zero.

Because and tend to zero as h tends to zero, the bracketed terms tend to zero as h tends to zero.

Because the porosity of the surface soil results in virtually zero runoff, lenses are easily polluted by fecal waste, burials, and chemical spills.

Because complex differentiation is linear and obeys the product, quotient, and chain rules, the sums, products and compositions of holomorphic functions are holomorphic, and the quotient of two holomorphic functions is holomorphic wherever the denominator is not zero.

Because of the weak, induced dipole-dipole interaction between helium atoms, their macroscopic physical properties are mainly determined by their zero point energy (" ground state kinetic energy ").

Because of this sensitivity to infant mortality, simple life expectancy at age zero can be subject to gross misinterpretation, leading one to believe that a population with a low overall life expectancy will necessarily have a small proportion of older people.

Because the full-time code messages requires that the most significant bits of each byte are zero ( valid MIDI data bytes ), there are really only 28 available bits and 4 spare bits.

Because the camshaft speed is nearly zero before the engine is started, an electric pump is used.

Because both ends of the RS-232 circuit depend on the ground pin being zero volts, problems will occur when connecting machinery and computers where the voltage between the ground pin on one end, and the ground pin on the other is not zero.

Because the low pressure stages are limiting the flow, the high pressure stages can be fixed to zero flow.

Because of this, many formulas in algorithms ( such as that for calculating hash table indices ) can be elegantly expressed in code using the modulo operation when array indices start at zero.

Because the left-hand side of the equation is a sum of the squares of real numbers it is greater than or equal to zero, thus:

Because of the proximity to the sea, freezing temperatures are rare ; an average of 2. 9 days a year, and lasting frosts ( when the maximum temperature remains less or equal to zero ) are non-existent.

Because a Trusted Computing equipped computer is able to uniquely attest to its own identity, it will be possible for vendors and others who possess the ability to use the attestation feature to zero in on the identity of the user of TC-enabled software with a high degree of certainty.

Because every hom-set Hom ( A, B ) is an abelian group, it has a zero element 0.

Because composition of morphisms is bilinear, the composition of a zero morphism and any other morphism ( on either side ) must be another zero morphism.

Because the divergence of the magnetic field is always zero due to the absence of magnetic monopoles, such an A can always be found.

Because this intensity is zero for zero pressure the method is relatively sensitive and accurate.