* Inverses: by definition every isomorphism has an inverse which is also an isomorphism, and since the inverse is also an endomorphism of the same object it is an automorphism.

He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory.

Philosophical aesthetics has not only to speak about art and to produce judgments about art works, but has also to give a definition of what art is.

This " institutional definition of art " ( see also Institutional Critique ) has been championed by George Dickie.

Ian Hacking ( 1999, p. 84 ) also uses the same definition.

The definition of ballroom dance also depends on the era: balls have featured popular dances of the day such as the Minuet, Quadrille, Polonaise, Polka, Mazurka, and others, which are now considered to be historical dances.

" The contains a simple and brief definition for the term bodhisattva, which is also the earliest known Mahāyāna definition.

The definition works without any changes if instead of vector spaces over a field F, we use modules over a commutative ring R. It also can be easily generalized to n-ary functions, where the proper term is multilinear.

This approach also allows preserving the curve definition under all linear or perspective 2D and 3D transforms and projections.

The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable.

Omnivores also consume both animal and non-animal food, and apart from the more general definition, there is no clearly defined ratio of plant to animal material that would distinguish a facultative carnivore from an omnivore, or an omnivore from a facultative herbivore, for that matter.

This definition was also often used outside the USSR during this period.

As Martin's definition suggests, the countercult ministries concentrate on non-traditional groups that claim to be Christian, so chief targets have been The Church of Jesus Christ of Latter-day Saints, Jehovah's Witnesses, Christian Science and the Unification Church, but also smaller groups like the Swedenborgian Church

A troll described in this work also influenced the D & D definition of that monster.

An intensional definition, also called a coactive definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set.

An extensional definition, also called a denotative definition, of a concept or term specifies its extension.

A recursive definition, sometimes also called an inductive definition, is one that defines a word in terms of itself, so to speak, albeit in a useful way.

The result, div F, is a function of p. From this definition it also becomes explicitly visible that div F can be seen as the source density of the flux of F.

However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.

" It also notes that "... no definition adequately specifies precise boundaries for the concept of ' mental disorder '... different situations call for different definitions ".

As such, it has to be distinguished from agricultural land, which, according to Food and Agriculture Organization's ( FAO ) definition, additionally includes land under permanent crops as well as permanent pastures.

* Brønsted-Lowry definition: Acids are proton ( H < sup >+</ sup >) donors, bases are proton acceptors ; this includes the Arrhenius definition.

* Lewis definition: Acids are electron-pair acceptors, bases are electron-pair donors ; this includes the Brønsted-Lowry definition.

However, the Russian culture has two distinct terms: Средняя Азия ( Srednjaja Azija or " Middle Asia ", the narrower definition, which includes only those traditionally non-Slavic, Central Asian lands that were incorporated within those borders of historical Russia ) and Центральная Азия ( Central ' naja Azija or " Central Asia ", the wider definition, which includes Central Asian lands that have never been part of historical Russia ).

Within this definition, it is of paramount importance that the term " file " includes directories.

This includes civil wars, however no specific definition of civil war is provided in the text of the Conventions.

Put informally, the definition includes the objects that have never crossed the orbit of Neptune.

Formally, this definition includes as classical all objects with the current orbits that

Unlike other schemes, this definition includes the objects with major semi-axis less than 39. 4 AU ( 2: 3 resonance ) – named Inner classical belt, or more than 48. 7 ( 1: 2 resonance ) – named Outer classical belt while reserving the term Main classical belt for the orbits between these two resonances.

An alcoholic beverage is a drink that contains ethanol, commonly known as alcohol ( although in chemistry the definition of " alcohol " includes many other compounds ).

Thus, an expanded definition for data warehousing includes business intelligence tools, tools to extract, transform and load data into the repository, and tools to manage and retrieve metadata.

If the XML document type declaration includes any SYSTEM identifier for the external subset, it can't be safely processed as standalone: the URI should be retrieved, otherwise there may be unknown named character entities whose definition may be needed to correctly parse the effective XML syntax in the internal subset or in the document body ( the XML syntax parsing is normally performed after the substitution of all named entities, excluding the five entities that are predefined in XML and that are implicitly substituted after parsing the XML document into lexical tokens ).

" Prior to Draper, Beauchamp & Davidson had also offered a definition which includes these elements, although they offered a somewhat longer account, and one that specifically discounts fetuses in order to distinguish between abortions and euthanasia:

There is also a broader definition, as described by Marc Bloch ( 1939 ), that includes not only warrior nobility but all three estates of the realm: the nobility, the clerics, and the peasantry bonds of manorialism ; this is sometimes referred to as a " feudal society ".

The phrase " feudal society " as defined by Marc Bloch expands on the definition proposed by Ganshof and includes within the feudal structure not only the warrior aristocracy bound by vassalage, but also the peasantry bound by manorialism, and the estates of the Church.

The definition of an internetwork today includes the connection of other types of computer networks such as personal area networks.

ISO 4217 includes codes not only for currencies, but also for precious metals ( gold, silver, palladium and platinum ; by definition expressed per one troy ounce, as compared to " 1 USD ") and certain other entities used in international finance, e. g. special drawing rights.

One argument based on incompatible properties rests on a definition of God that includes a will, plan or purpose and an existence outside of time.

Travis Jackson has also proposed a broader definition of jazz which is able to encompass all of the radically different eras: he states that it is music that includes qualities such as " swinging ", improvising, group interaction, developing an ' individual voice ', and being ' open ' to different musical possibilities ".

" The Stylebook definition of Latino includes not only persons of Spanish-speaking ancestry, but also more generally includes persons " from -- or whose ancestors were from --.

While many scientific experts might agree on a common definition of the term " coast ", the delineation of the extents of a coast differ according to jurisdiction, with many scientific and government authorities in various countries differing for economic and social policy reasons.

The unease and self-deception that characterized that period of colonial history would be revisited in many forms at political and social moments of crisis ( such as the Salem witch trials, which coincided with frontier warfare and economic competition among Indians and French and other European settlers ) and during lengthy periods of cultural definition ( such as the American Renaissance of the late 18th-and early 19th-century literary, visual, and architectural movements, which sought to capitalize on unique American identities ).

Extending the logic of these measures, Green adumbrated a positive and collectivist definition of liberty, a concept of " public freedom " that justified legislative oversight of economic life, especially land ownership and use.

But this debate is more about basic economic theory ( the role of the factors in the economy ) than it is about the definition of the factors of production.

The International Accounting Standards Board ( IASB ) uses the following definition: " Income is increases in economic benefits during the accounting period in the form of inflows or enhancements of assets or decreases of liabilities that result in increases in equity, other than those relating to contributions from equity participants.

In recent years, economic or industrial espionage has taken on an expanded definition.

The goal was to create a clear definition of economic freedom and a method for measuring it.

This definition is in accord with the view that political change is important for responding to economic, ecological and cultural challenges.

The legal definition and the economic definition of taxes differ in that economists do not consider many transfers to governments to be taxes.

An economic definition, by Atkinson, states that "... direct taxes may be adjusted to the individual characteristics of the taxpayer, whereas indirect taxes are levied on transactions irrespective of the circumstances of buyer or seller.

This definition provided a way of broadly categorizing the nations of the earth into three groups based on social, political, and economic divisions.

Under the first definition, each depression will always coincide with a recession, since the difference between a depression and a recession is the severity of the fall in economic activity.

An important base for the first definition of market socialism in economic theory is the Lange Model, which states that an economy in which all production is performed by the state, but in which there is a functioning price mechanism, has similar properties to a market economy under perfect competition, in that it achieves Pareto efficiency.

That was the second successive quarter of negative economic growth, which is the definition of a recession.

In this definition, it is the active participation of the population as a whole, and workers in particular, in the management of economy that characterises democratic socialism, while nationalisation and economic planning ( whether controlled by an elected government or not ) are characteristic of state socialism.

The essential elements of CoSGOP are analysis of stakeholders ( identifying stakeholders ’ perceptions of problems, interests, and expectations ); analysis of problems and potentials ( including objective problems and problems and potentials perceived by stakeholders ); development of goals, improvement priorities, and alternatives ( requiring intensive communication and active stakeholder participation ); specification of an improvement program and its main activities ( based on priorities defined with the stakeholders ); assessment of possible impacts of the improvement program ; definition and detailed specification of key projects and their implementation ; continuous monitoring of improvement activities, feedback, and adjustment of the programme ( including technical and economic information and perceptions of stakeholders ).

Scholars outside China see this re-working of the definition of Maoism as providing an ideological justification for what they see as the restoration of the essentials of capitalism in China by Deng and his successors, who sought to " eradicate all ideological and physiological obstacles to economic reform ".

A classic definition influenced by Kenneth Arrow and James Meade is provided by Heller and Starrett ( 1976 ), who define an externality as “ a situation in which the private economy lacks sufficient incentives to create a potential market in some good and the nonexistence of this market results in losses of Pareto efficiency .” In economic terminology, externalities are examples of market failures, in which the unfettered market does not lead to an efficient outcome.

The modern phenomenon of extensive suburban growth, satellite urban development, and migration of city-dwellers to villages have further complicated the definition of towns, creating communities urban in their economic and cultural characteristics but lacking other characteristics of urban localities.

There is not one single definition for a mixed economy, but the definitions always involve a degree of private economic freedom mixed with a degree of government regulation of markets.

Essentially, economic neoliberalism can be derived by taking the classical neoliberal definition above and taking the protected personal sphere to solely refer to property rights and contract.

The definition of economic neoliberalism which has been presented focuses heavily on economic policies and has little to say about non-economic policy ( other than that they should not be allowed to interfere with the running of the free market ).