Falling somewhere in a category between Einstein's theory and sand fleas -- difficult to see but undeniably there, nevertheless -- is the tropical green `` city '' of Islandia, a string of offshore islands that has almost no residents, limited access and an unlimited future.

It is natural from the marksman's viewpoint to call a bull's-eye a success, but in the mice example it is arbitrary which category corresponds to straight hair in a mouse.

In the third category the function is double-valued in this interval.

When alienation is used as an objective and diagnostic category, for example, it becomes clear that Fromm would have to say that awareness of alienation goes far toward conquering it.

There is a difference between evidence and illustration, and Fromm's citation of the other diagnosticians fits the latter category.

It is the only county in the state so far this month reporting a possible shortage in GA category, for which emergency allotment can be given by the state if necessary.

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 ).

For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms ( usually called a small category ), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets.

Abjads differ from abugidas, another category invented by Daniels, in that in abjads, the vowel sound is implied by phonology, and where vowel marks exist for the system, such as nikkud for Hebrew and harakāt for Arabic, their use is optional and not the dominant ( or literate ) form.

Abandoned land resulting from shifting cultivation is not included in this category.

The most general setting in which these words have meaning is an abstract branch of mathematics called category theory.

In category theory, an automorphism is an endomorphism ( i. e. a morphism from an object to itself ) which is also an isomorphism ( in the categorical sense of the word ).

This is a very abstract definition since, in category theory, morphisms aren't necessarily functions and objects aren't necessarily sets.

The automorphism group of an object X in a category C is denoted Aut < sub > C </ sub >( X ), or simply Aut ( X ) if the category is clear from context.

On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.

Parmenides reasoned that if everything is identical to being and being is a category of the same thing then there can be neither differences between things nor any change.

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.

All cars in the category use identical spool differentials, brake packages and gearboxes.

This act is one in a category of regulatory enactments which attempt to control price discriminations — or different prices for identical products.

It has been suggested that there is no validity to the term " second-generation antipsychotic drugs " and that the drugs that currently occupy this category are not identical to each other in mechanism, efficacy, and side-effect profiles:

This expanded the PCs presence in homes, replacing the home computer category during the 1990s and leading to the current monoculture of architecturally identical personal computers.

An auto-equivalence of a category C is an equivalence F: C → C. The auto-equivalences of C form a group under composition if we consider two auto-equivalences that are naturally isomorphic to be identical.

Two isomorphic categories share all properties that are defined solely in terms of category theory ; for all practical purposes, they are identical and differ only in the notation of their objects and morphisms.

Although the axioms defining a single semigroup are almost identical to those defining a category, one frequently assumes many additional facts about the relationship between categories ( functors between them exist, natural transformations between these functors exist, the functors themselves form a category, and so on ).

The name is taken from the mathematical monad construct in category theory, though the two concepts are not identical.

To deal with this shortage of direct data, the board provided a second level of inputs that can be applied in three situations: The first involves less-active markets for identical assets and liabilities ; this category is ranked lower because the market consensus about value may not be strong.

F-Script is based on a pure object paradigm ( every entity manipulated within the language is an object ), its base syntax and concepts being identical to those of Smalltalk ( the canonical example of the category ) with specific extensions to support array programming as in the APL programming language.

This category contains articles on pairs of identical twins, and people who were born with an identical twin.

" The FAA was able to slither out from under their written promises, leaving the employees they had brought into the then-new AOS directorate without benefit of the massive pay increases conferred upon nearly all other FAA employees of identical job category in 1998.

A category is called skeletal if isomorphic objects are necessarily identical.

One-make racing ( known as spec racing in North America ) is a racing category in which all competitors race in identical or very similar vehicles from the same manufacturer, often using the same model.

Non-Israeli residents of the West Bank and the Gaza Strip were issued ID cards by the Civil Administration of Judea and Samaria ( and Gaza until 2005 ), which had an almost identical layout as the Israeli card ( the differences being that the surname category came after the first name, father's name, and grandfather's name categories instead of at the top, and the " ethnicity " category was replaced with a " religion " category ).

Category: Higher category theory

To fulfill requirement 2b, the candidate must score one GM norm in a category 1a tournament or two norms within a three year period in two Category 1b tournaments, or one Category 2a tournament and one Category 1b tournament.

Category: Limits ( category theory )

Category theory, another field within " foundational mathematics ", is rooted on the abstract axiomatization of the definition of a " class of mathematical structures ", referred to as a " category ".

; Category of topological spaces: The category Top has topological spaces as objects and continuous maps as morphisms.

Katrina was a Category 3 hurricane when it struck although it had been a category 5 hurricane in the Gulf of Mexico.

Category: Objects ( category theory )

Category theorists will often think of the ring R and the category R as two different representations of the same thing, so that a particularly perverse category theorist might define a ring as a preadditive category with exactly one object ( in the same way that a monoid can be viewed as a category with only one object-and forgetting the additive structure of the ring gives us a monoid ).

Category: Limits ( category theory )

Category: Limits ( category theory )

Today, hurricane force winds are sometimes described as Beaufort scale 12 through 16, very roughly related to the respective category speeds of the Saffir – Simpson Hurricane Scale, by which actual hurricanes are measured, where Category 1 is equivalent to Beaufort 12.

* Web Category Analysis Tool ( WebCAT )-lets the usability engineer construct and conduct a web category analysis

Category: Higher category theory

* Category killers or Category Specialist: By supplying wide assortment in a single category for lower prices a retailer can " kill " that category for other retailers.

Propranolol, like other beta blockers, is classified as Pregnancy category C in the United States and ADEC Category C in Australia.

* See: Category: Members of the United States Securities and Exchange Commission for alphabetized list of members who have articles written about them and who have the appropriate category marker on their page.

To browse this category tree, start at: Category: Korea.