[permalink] [id link]

Conversely, if F is left adjoint to G, and G is naturally isomorphic to G ′ then F is also left adjoint to G ′.

from
Wikipedia

## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered which contradicted a cherished theory

**,**the sources were denounced as faulty.

__Conversely__

**,**experimenters would consider as impressive such statements as the following

**,**which

**,**

__if__they turned out

**to**be hits

**,**are so unusual as

**to**be really significant:

__Conversely__

**,**

__if__he gives a heavy rating

**to**his own reading

**,**

**and**finds more accurate facts in it than in the others

**,**a point

**is**chalked up for the intrinsic

**,**objective meaningfulness of this type of mediumistic material.

__Conversely__

**,**a subset R defines a binary function

__if__

**and**only

__if__

**,**for any x in X

**and**y in Y

**,**there exists a unique z in Z such that ( x

**,**y

**,**z ) belongs

**to**R.

__Conversely__

**,**

__if__a Boolean ring A

**is**given

**,**we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y )

**and**x ∧ y := x · y.

__Conversely__

**,**

__if__the second theory

**is**correct

**,**

**then**the Athenians were merely reacting

**to**the Persians attacking them.

__Conversely__the equilibrium position

**is**said

**to**be " far

**to**the

**left**"

__if__hardly any product

**is**formed from the reactants.

__Conversely__

**,**

__if__ƒ: C → C

**is**a function which

**is**differentiable when regarded as a function on R < sup > 2 </ sup >,

**then**ƒ

**is**complex differentiable

__if__

**and**only

__if__the Cauchy – Riemann equations hold.

__Conversely__

**,**

__if__the amount of fat

**is**increased

**,**increasing the number of calories ingested will only add weight.

__Conversely__

**,**

__if__the source of waves

**is**moving away from the observer

**,**each wave

**is**emitted from a position farther from the observer than the previous wave

**,**so the arrival time between successive waves

**is**increased

**,**reducing the frequency.

__Conversely__every partition of comes from an equivalence relation in this way

**,**according

**to**which

__if__

**and**only

__if__

**and**belong

**to**the same set of the partition.

If neither A nor B includes the idea of existence

**,****then**" some A are B " simply adjoins A**to**B.__Conversely__**,**__if__A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal**to**two right angles ",**then**" A exists "**is**automatically true**,****and**we have an ontological proof of A's existence.__Conversely__

**,**

__if__the measured potential

**is**negative

**,**the electrode

**is**more oxidizing than the SHE ( such as Zn in ZnSO < sub > 4 </ sub > where the standard electrode potential

**is**− 0. 76 V ).

__Conversely__

**,**

__if__the firm

**is**able

**to**get bulk discounts of an input

**,**

**then**it could have economies of scale in some range of output levels even

__if__it has decreasing returns in production in that output range.

__Conversely__

**,**daylight stock shot in daylight will look normal

**,**but orange

__if__shot under tungsten lights.

__Conversely__

**,**

__if__the data are sparse — that

**is**

**,**

__if__only K out of N Fourier coefficients are nonzero —

**then**the complexity can be reduced

**to**O ( K log N log ( N / K )),

**and**this has been demonstrated

**to**lead

**to**practical speedups compared

**to**an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients

**to**several decimal places ).

Conversely and F

Given a field ordering ≤ as in Def 1

**,**the elements such that x ≥ 0 forms a positive cone of__F__.__Conversely__**,**given a positive cone P of__F__as in Def 2**,**one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y**to**mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.__Conversely__

**,**

**if**A

**is**invertible

**,**

__F__

**is**algebraically closed

**,**

**and**A < sup > n </ sup >

**is**diagonalizable for some n that

**is**not an integer multiple of the characteristic of

__F__

**,**

**then**A

**is**diagonalizable.

*

__Conversely__**,****if****is**such that**and**are purely inseparable extensions**,****then**E**is**purely inseparable over__F__.__Conversely__

**,**a connection on E determines a connection on

__F__( E ),

**and**these two constructions are mutually inverse.

__Conversely__

**,**given a Hopf algebra whose coalgebra structure

**is**given above

**,**we can recover a formal group law

__F__from it.

__Conversely__

**,**Oymyakon on July 28

**,**2010 recorded a record high temperature of

**,**yielding a temperature range of 105. 8 ° C ( 190. 4 °

__F__).

__Conversely__

**,**

**if**

__F__has characteristic zero

**,**

**then**given an homogeneous polynomial ƒ of degree n on V

**,**the polarization of ƒ

**is**a multilinear function on the n-th Cartesian product of V. The polarization

**is**defined by

__Conversely__

**,**given any element u ∈

__F__( A ) we may define a natural transformation Φ: Hom ( A ,–) →

__F__via

Conversely and is

__Conversely__

**,**an adiabatic process that

__is__irreversible

**and**extracts no work

__is__in an isenthalpic process

**,**such as viscous drag

**,**progressing towards a nonnegative change in entropy.

__Conversely__

**,**British English favours fitted as the past tense of fit generally

**,**whereas the preference of American English

__is__more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts

**,**AmEng uses fitted for the sense of having made an object conform

**to**an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform

**to**an unchanged object that surrounds it ( e. g., " fit X into Y ");

**and**for the spatial senses ( both intransitive

**and**transitive ) of having been matching with respect

**to**contour

**,**with no alteration of either object implied

**,**AmEng prefers fit (" The clothes fit.

__Conversely__the use of true brass seems

**to**have declined in Western Europe during this period in favour of gunmetals

**and**other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in the manufacture of coins in Northumbria

**and**there

__is__archaeological

**and**historical evidence for the production of brass in Germany

**and**The Low Countries areas rich in calamine ore which would remain important centres of brass making throughout the medieval period

**,**especially Dinant – brass objects are still collectively known as dinanterie in French.

__Conversely__

**,**because space

__is__expanding

**,**

**and**more distant objects are receding ever more quickly

**,**light emitted by us today may never " catch up "

**to**very distant objects.

__Conversely__

**,**modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined

**and**dependent on the methods developed through biotechnology

**and**what

__is__commonly thought of as the life sciences industry.

__Conversely__

**,**the islands do not receive the upwellings ( cold streams ) that affect the West African coast

**,**so the air temperature

__is__cooler than in Senegal

**,**but the sea

__is__actually warmer

**,**because the orographic relief of some islands

**,**as Sao Miguel with steep mountains

**,**cover it with rich woods

**and**luxuriant vegetation where the dense moisture condense

**and**soak the plants

**,**rocks

**,**soil

**,**logs

**,**moss etc.

__Conversely__in francophone Canada

**,**one hundredth of a Canadian dollar

__is__informally called a sou ( penny ), though cent

__is__official in both English

**and**French.

__Conversely__

**,**an absence of secure cycle-parking

__is__a recurring complaint by cyclists from cities with low modal share of cycling.

* The spectrum of any bounded linear operator on a Banach space

__is__a nonempty compact subset of the complex numbers C.__Conversely__**,**any compact subset of C arises in this manner**,**as the spectrum of some bounded linear operator.0.122 seconds.