* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

Duality with pluralism is considered a logical fallacy.

Duality is also sometimes called reciprocity or polarity.

Duality is most commonly defined in terms of polar reciprocation about a concentric sphere.

Duality ( opposition ) that creates the energy ( or libido ) of the psyche, which Jung asserts expresses itself only through symbols: " It is the energy that manifests itself in the life process and is perceived subjectively as striving and desire.

Xiuhtecuhtli is a manifestation of Ometecuhtli, the Lord of Duality, and according to the Florentine Codex Xiuhtecuhtli was considered to be mother and father of the Gods, who dwelled in the turquoise enclosure in the center of earth.

This paradox is known as the Wave – particle Duality Paradox.

** The interview was also sampled in Konkhra's track " Religion is a Whore " and The Faceless's " Planetary Duality.

Duality is the observation that σ is true for some category C if and only if σ < sup > op </ sup > is true for C < sup > op </ sup >.

According to Giddens there is a " Duality of structure " by which social practice, which is the principal unit of investigation, has both a structural and an agency-component.

If the Star Goddess is the great Unity, than the Twins can be seen as representing all Duality.

Duality in the projective plane is a special case of duality for projective spaces, transformations of PG ( n, K ) ( also denoted by KP < sup > n </ sup >) with K a field, that interchange objects of dimension r with objects of dimension n-1-r ( = codimension r + 1 ).

The fact that this is an isomorphism of chain complexes is a proof of Poincaré Duality.

This result is an application of Poincaré Duality together with the Universal coefficient theorem which gives an identification and.

Poincaré Duality is closely related to the Thom Isomorphism Theorem, as we will explain here.

The Lotus Sutra's parable of the Burning House implies that all talk of Duality or Non-Duality by Buddhas and Bodhisattvas is merely Skillful Means ( Sanskrit upaya kausala ) meant to lead the deluded to a much higher truth.

Formally, this is captured by the Duality Principle for ordered sets:

Duality of polytopes and order-theoretic duality are both involutions: the dual polytope of the dual polytope of any polytope is the original polytope, and reversing all order-relations twice returns to the original order.

* E. H. Carlson, Wave – Particle Duality: Light on Project PHYSNET

* Duality: Language works on two levels at once, a surface level and a semantic ( meaningful ) level.

Duality also reached # 137 on the Billboard 200, and also # 2 for 18 weeks on Heatseekers Albums.

*" Xenochrist ", a song on the album Planetary Duality by The Faceless

Duality first appeared for actions of the reals in the work of Connes and Takesaki on the classification of Type III factors.

In Chinese creation myth | Daoist creation myth, " The Way gave birth to unity, Unity gave birth to duality, Duality gave birth to trinity, Trinity gave birth to the myriad creatures.

Originally shamanistic practices that have over time may once have been monotheistic later once since deification of an Earth Mother to the Sky father as a Duality, also including ancestor worship and an addition for a " sun deity ", polytheizing the religion and more deities were incorporated after-wards.

Third-Wave Feminism and the Need to Reweave the Nature / Culture Duality, NWSA Journal 16 ( 3 ): 154-179.

Miguel Leon-Portilla interprets the name " Ometeotl " as " Lord of the Duality " and argues that Ometeotl was the supreme creator deity of the Aztecs, and that the Aztecs envisioned this deity as a mystical entity with a dual nature akin to the European concept of the trinity.

Duality and unity are both significant.

Duality implies distinctive cultural development while unity implies common purpose and community.

* Duality in field theory and statistical systems, Robert Savit, Rev.

* Berthold-Georg Englert, Marlan O. Scully & Herbert Walther, Quantum Optical Tests of Complementarity, Nature, Vol 351, pp 111 – 116 ( 9 May 1991 ) and ( same authors ) The Duality in Matter and Light Scientific American, pg 56 – 61, ( December 1994 ).

Gerrard teamed with Pieter Bourke ( Snog, Soma ) to issue Duality in April 1998.

Duality in the Fano plane: Each point corresponds to a line and vice versa.

* B. R. Greene and M. R. Plesser, " Duality in Calabi-Yau Moduli Space ".

In spots such as the elbows and knees the second skin is worn off and I realized the aborigines were much darker than they appeared ; ;

It is said that, even at the present stage of Southern urbanization, such a city as Atlanta is not distinctly unlike Columbus or Trenton.

Has the agrarian tradition become such an addiction that the switch to urbanism is somehow dreaded or unwanted??

and the success of such an endeavor is, as suggested above, glaringly rare.

Obviously, such a Northern tourist's purpose is somewhat akin to a child's experience with Disneyland: he wants to see a world of make-believe.

Yet his concern even here is with a slowly changing socio-economic order in general, and he never deals with such specific aspects of this change as the urban and industrial impact.

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

We are desperately in the need of such invention, for man is still very much at the mercy of man.

I knew that a conversation with the author would not settle such questions, because a man is not the same as his writing: in the last analysis, the questions had to be settled by the work itself.

It only means that there will be new form, and that this form will be of such a type that it admits the chaos and does not try to say that the chaos is really something else.

Within this notion clarity is possible, but for us who are neither Greek nor Jansenist there is not such clarity.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.

After how many generations is such wealth ( mounting all the while through the manipulations of high finance ) purified of taint??

It consists of fragmentary personal revelations, such as `` The Spark '': `` There is a spark dwells deep within my soul.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Noting such evidence is the first step ; ;

There is no justification for such misrepresentation.

But what a super-Herculean task it is to winnow anything of value from the mud-beplastered arguments used so freely, particularly since such common use is made of cliches and stereotypes, in themselves declarations of intellectual bankruptcy.

Yet the attitude that the fate of the Presidency demands in such a situation is quite distinct from the simple courage that can proceed with battles to be fought, regardless of the consequences.