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

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## Some Related Sentences

Duality and theorem

The Principle of Plane

__Duality__says that dualizing any__theorem__**in****a**self-dual projective plane C produces another__theorem__valid**in**C.
This result

**is**an application of Poincaré__Duality__together with**the**Universal coefficient__theorem__**which**gives an identification and.

Duality and definition

**:**From

**the**point of view of

**the**

__definition__

**,**this

**is**an expression of

**the**Poincaré

__Duality__isomorphism where

**is**

**the**quotient of

**the**field of fractions of

**by**

**,**considered as a-module

**,**and where

**is**

**the**conjugate-module to ie

**:**as an abelian group it

**is**identical to but

**the**covering transformation acts

**by**.

Duality and category

__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 >.

__Duality__theorems of Tannaka and Krein describe

**the**converse passage from

**the**

__category__Π ( G ) back to

**the**group G

**,**allowing one to recover

**the**group from its

__category__of representations.

Duality and theory

This formulation of Poincaré

__Duality__**has**become quite popular as it provides**a**means to define Poincaré__Duality__for any generalized homology theories provided one**has****a**Thom Isomorphism for that homology__theory__.*****

__Duality__principle

**in**functional analysis

**,**used

**in**

**the**large sieve method of analytic number

__theory__

A treatment of this

__theory__**,**Residues and__Duality__( 1966 )**by**Robin Hartshorne**,**became an accessible reference.

Duality and has

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.

Duality and dual

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__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.

Duality and which

__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.

**"**After

**the**Red Dwarf crew finds

**the**wreck it

**is**brought aboard and repaired

**in**order to utilise its

__Duality__Jump engine

**,**

__which__could get

**the**crew back to Earth within three months.

Duality and is

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.
** The interview was also sampled

**in**Konkhra's track**"**Religion__is__**a**Whore**"**and The Faceless's**"**Planetary__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 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.

Duality and by

*****Blackadder

**:**

**"**The Black Seal

**"**( 1983 ),

**"**Chains

**"**( 1986 ),

**"**Duel and

__Duality__

**"**( 1987 ) — Along with

**"**Goodbyeee

**"**( 1989 ),

**the**final episodes of

**the**Blackadder series took

**a**liberty that many series would be unable to take

**,**

__by__killing off

**the**major characters ( apart from

**in**Blackadder

**the**Third when only Prince George died ).

Duality and ".

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