* 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 ".

The official definition of " planet " used by the International Astronomical Union ( IAU ) only covers the Solar System and thus does not apply to exoplanets.

The term covers large paintings in oil on canvas or fresco produced between the Renaissance and the late 19th century, after which the term is generally not used even for the many works that still meet the basic definition.

Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

The definition also covers activities which would fall within the traditional definition of money laundering as a process by which proceeds of crime are concealed or disguised so that they may be made to appear to be of legitimate origin.

The UNRWA has a much broader definition of " refugee " than the UNCHR, including not only refugees themselves but their descendants in perpetuity ; however, it only covers refugees stemming from the 1948 and 1967 Arab-Israeli wars.

It covers the requirements definition, the systems architecture, the behavior modeling and the virtual product or embedded software generation.

# Lifting covers up the definition of translation, which means moving something from one point in space to another.

and the corresponding u are purely radiative, since the dissipation term, (− J • E ) covers the total current, while the definition in terms of H has contributions from bound currents which then lack in the dissipation term.

This covers a far more narrow definition of Mayfair, Soho, and parts of Fitzrovia and Marylebone.

" A basic definition of a global circumnavigation would be a route which covers at least a great circle, and in particular one which passes through at least one pair of points antipodal to each other.

The postcode " W11 ", centred on the Post Office in Westbourne Grove, near the junction with Denbigh Road, is the one most closely associated with Notting Hill, although the postcode immediately to the north, " W10 ", covers that part of North Kensington which would fall within a broader definition.

That definition covers email hosting services, as well as ( the relevant department of ) companies, universities, organizations, groups, and individuals that manage their mail servers themselves.

The Fire Department's district covers a larger geographic area than the CSD and is more nearly equivalent to the El Dorado County definition of the El Dorado Hills Community Region.

FDIC deposit insurance covers deposit accounts, which, by the FDIC definition, include:

This definition encourages the belief that pansexuality is the only category that covers individuals who do not cleanly fit into the categories of male / man or female / woman.

The cladogram covers the group as defined under Gauthier's definition.

Under a more restrictive definition, the peninsula covers an area of about.

This broader definition of webmaster covers not only technical aspects of overseeing website construction and maintenance, but also managing website content, advertising, marketing, and order fulfillment.

The latter definition encompasses many modern structures, while the former more generally covers tunnel systems from ancient times to the present day.

This article also covers lifting machines that do not strictly fit the above definition of a crane, but are generally known as cranes, such as stacker cranes and loader cranes.

Others see the classic period as overlapping the vintage period, especially since the vintage designation covers all vehicles produced in the period while the official classic definition does not, only including high-end vehicles of the period.

The remainder of this article covers Quideau and WBSSH polyphenols, with the former providing the least restrictive definition for including chemical substances and their activities in the discussion.

" The EU's definition of an orphan condition is broader than that of the USA, in that it also covers some tropical diseases that are primarily found in developing nations.

UNRWA's definition of a refugee also covers the descendants of persons who became refugees in 1948.