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Conversely, the following characterization of derived functors holds: given a family of functors R < sup > i </ sup >: A → B, satisfying the above, i. e. mapping short exact sequences to long exact sequences, such that for every injective object I of A, R < sup > i </ sup >( I )= 0 for every positive i, then these functors are the right derived functors of R < sup > 0 </ sup >.

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## Some Related Sentences

Conversely and following

__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__

**,**

**the**Roman poet Ovid provides

**a**second etymology

**,**in which he says

**that**

**the**month

**of**May is named

**for**

**the**maiores

**,**Latin

**for**" elders ," and

**that**

**the**

__following__month ( June ) is named

**for**

**the**iuniores

**,**or " young people " ( Fasti VI

**.**88 ).

__Conversely__

**,**surveys conducted among living donors postoperatively and in

**a**period

**of**five years

__following__

**the**procedure have shown extreme regret in

**a**majority

**of**

**the**donors

**,**who said

**that**

**given**

**the**chance

**to**repeat

**the**procedure

**,**they would not

**.**

__Conversely__

**,**serum resistin levels have been found

**to**decline with decreased adiposity

__following__medical treatment

**.**

__Conversely__

**,**Hill would play only 47 games in

**the**

__following__four seasons due

**to**

**a**recurring ankle injury

**.**

Lund said

**:**__Conversely__**,****the**majority opinion was criticized by Harvard University law professor Alan Dershowitz**,**who wrote**:**Some critics**of****the**decision argue**that****the**majority seemed**to**seek refuge from their own logic in**the**__following__sentence in**the**majority opinion**:**" Our consideration is limited**to****the**present circumstances**,****for****the**problem**of**equal protection in election processes generally presents many complexities**.**__Conversely__

**,**

__following__

**the**diurnal motion with

**the**camera

**,**

**to**eliminate it on

**the**photograph

**,**can best be done with an equatorial mount

**,**which requires adjusting

**the**

**right**ascension only ;

**a**telescope may have

**a**motor

**to**do

**that**automatically ( sidereal drive ).

__Conversely__

**,**

__following__

**the**suicide

**of**Adolf Hitler

**,**de Valera

**,**

__following__diplomatic protocol

**,**controversially offered condolences

**to**

**the**German ambassador

**.**

__Conversely__

**,**one may argue

**that**

**the**true meaning

**of**IVT

**,**even in classical mathematics

**,**is

**the**constructive version involving

**the**locally non-zero condition

**,**with

**the**full IVT

__following__by " pure logic " afterwards

**.**

__Conversely__

**,**

**the**United States

**,**which did not enter

**the**war until December 7

**,**1941

**,**

__following__

**the**Attack on Pearl Harbor

**,**instituted

**the**Selective Service Act on September 14

**,**1940 and extended it by

**a**single vote

**the**

__following__year

**.**

__Conversely__

**,**

**the**Indonesian cuisine also had influenced colonial Dutch and Indo people

**that**brought Indonesian dishes back

**to**

**the**Netherlands due

**to**repatriation

__following__

**the**independence

**of**Indonesia

**.**

__Conversely__

**,**

**to**send

**the**caller number on

**a**line where

**the**number is normally withheld

**,**

**the**

__following__prefixes can be dialled

**:**

__Conversely__

**,**serum resistin levels have been found

**to**decline with decreased adiposity

__following__medical treatment

**.**

__Conversely__

**,**in Mechanicsburg

**,**she is confronted by Vole

**,**

**a**rogue Jäger who is actively trying

**to**kill her and subvert Gil ;

**the**extent

**to**which Vole is working with

**the**Baron

**,**instead

**of**

__following__his own anti-Heterodyne agenda

**,**has not yet been fully revealed

**.**

__Conversely__

**,**Bhāgavata teaches

**that**simply

__following__Vedic injunctions

**that**do not produce devotion towards God

**are**

**of**transitory benefit and

**are**fruitless labour

**.**

__Conversely__

**,**her contributions

**to**Japanese education were recognized by

**the**

__following__Imperial Awards

**:**

__Conversely__

**,**it was stated

**that**drivers often ran through Salisbury very fast on

**these**trains

**to**" get

**a**run " at

**the**

__following__hill

**.**

__Conversely__

**,**there is

**a**tendency

**to**be much more sympathetic

**to**those who satisfy any

**of**

**the**

__following__conditions

**:**

__Conversely__

**,**when

**a**fight is not playing in MegaMan's favor

**,**unless in

**a**doublesoul

**,**he gains an anxious expression and

__following__this

**,**Darkchips begin

**to**display themselves in

**the**Custom Screen

**.**

__Conversely__

**,**

**the**Persian kings could

**,**and did

**,**destroy

**the**shrines

**of**peoples who had rebelled against them

**,**as happened at Miletos in 494 BC

__following__

**the**Ionian Revolt

**.**

Conversely and derived

__Conversely__

**,**peptides

__derived__from HR1 have little viral inhibition efficacy due

**to**

**the**propensity

**for**

**these**peptides

**to**aggregate in solution

**.**

Conversely and holds

__Conversely__

**,**externalism

__holds__

**that**it is things about

**the**world which motivate us

**,**justify our beliefs

**,**determine meaning

**,**etc

**.**

__Conversely__

**,**simply having negative relationships with some women does not necessarily mean someone

__holds__misogynistic views

**.**

If f is flat

**,****then**.< ref**>**EGA IV**<**sub**>**2**</**sub >, Corollaire 6**.**1**.**2 .</ ref**>**__Conversely__**,**if this equality__holds__**for**all x**,**X is Cohen-Macaulay**,**and Y is regular**,****then**f is flat .< ref**>**EGA IV**<**sub**>**2**</**sub >, Proposition 6**.**1**.**5**.**__Conversely__

**,**if this identity

__holds__in

**a**ring

**R**

**for**all pairs

**of**elements

**a**and b

**of**

**the**ring

**,**

**then**

**R**is commutative

**.**

__Conversely__

**,**

**a**business can have negative net assets showing on its balance sheet but still be cash-flow solvent if ongoing revenue is able

**to**meet debt obligations

**,**and thus avoid default

**:**

**for**instance

**,**if it

__holds__

**long**term debt

**.**

Conversely and given

__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__

**,**there

**are**other stars

**that**never rise

**above**

**the**horizon

**,**as seen from any

__given__point on

**the**Earth's surface ( except exactly on

**the**equator ).

__Conversely__

**,**

__given__

**a**groupoid G in

**the**algebraic sense

**,**let G

**<**sub

**>**

**0**

**</**sub

**>**be

**the**set

**of**all elements

**of**

**the**form x * x

**<**

**sup**>− 1

**</**

**sup**

**>**with x varying through G and define G ( x * x

**<**

**sup**>-1

**</**

**sup**>, y * y

**<**

**sup**>-1

**</**

**sup**>) as

**the**set

**of**all elements f

**such**

**that**y * y

**<**

**sup**>-1

**</**

**sup**

**>*** f * x * x

**<**

**sup**>-1

**</**

**sup**

**>**exists

**.**

__Conversely__

**,**

__given__central idempotents

**a**

**<**sub

**>**1

**</**sub >,...,

**a**

**<**sub

**>**n

**</**sub

**>**in

**R**

**that**

**are**pairwise orthogonal and have sum 1

**,**

**then**

**R**is

**the**direct sum

**of**

**the**rings Ra

**<**sub

**>**1

**</**sub >,…, Ra

**<**sub

**>**n

**</**sub

**>.**

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__

**,**only

**the**wiki users interested in

**a**

__given__project need look at its associated wiki pages

**,**in contrast

**to**high-traffic mailing lists which may burden subscribers with many messages

**,**regardless

**of**their relevance

**.**

__Conversely__

**,**

__given__

**a**harmonic function

**,**it is

**the**real part

**of**an analytic function

**,**( at least locally ).

Each convex set containing X must ( by

**the**assumption**that**it is convex ) contain all convex combinations**of**points in X**,**so**the**set**of**all convex combinations is contained in**the**intersection**of**all convex sets containing X**.**__Conversely__**,****the**set**of**all convex combinations is itself**a**convex set containing X**,**so it also contains**the**intersection**of**all convex sets containing X**,**and therefore**the**sets__given__by**these**two definitions must be equal**.**__Conversely__

**,**

__given__an ordered tree

**,**and conventionally draw

**the**root at

**the**top

**,**

**then**

**the**child nodes in an ordered tree can be drawn left-to-right

**,**yielding an essentially unique planar embedding ( up

**to**embedded homotopy

**,**

**i**

**.**

**e**., moving

**the**edges and nodes without crossing ).

__Conversely__

**,**

**the**influence

**of**

**the**data at any

__given__point on

**the**initial line propagates with

**the**finite velocity c

**:**there is no effect outside

**a**triangle through

**that**point whose sides

**are**characteristic curves

**.**

__Conversely__

**,**

__given__any harmonic function in two dimensions

**,**it is

**the**real part

**of**an analytic function

**,**at least locally

**.**

__Conversely__

**,**if (

**A**

**,**m

**,**

**e**

**,**inv ) is

**a**group

**object**in one

**of**those categories

**,**

**then**m necessarily coincides with

**the**

__given__operation on

**A**

**,**

**e**is

**the**inclusion

**of**

**the**

__given__identity element on

**A**

**,**inv is

**the**inversion operation and

**A**with

**the**

__given__operation is an abelian group

**.**

__Conversely__

**,**if

**the**Turing Machine is expected polynomial-time (

**for**any

__given__x ),

**then**

**a**considerable fraction

**of**

**the**runs must be polynomial-time bounded

**,**and

**the**coin sequence used in

**such**

**a**run will be

**a**witness

**.**

__Conversely__

**,**

__given__any ring

**,**we can form

**a**category by taking objects

**A**

**<**sub

**>**n

**</**sub

**>**indexed by

**the**set

**of**natural numbers ( including zero ) and letting

**the**hom-set

**of**morphisms from

**to**be

**the**set of-by-matrices over

**,**and where composition is

__given__by matrix multiplication

**.**

__Conversely__

**,**it is hard

**to**believe

**,**

__given__

**the**length and intensity

**of**

**the**struggle between Máel Sechnaill and Brian

**,**

**that**

**the**High King would surrender his title without

**a**fight

**.**

__Conversely__

**,**an algorithm

**to**test

**for**solvability in arbitrary integers could be used

**to**test

**a**

__given__equation

**for**solvability in natural numbers by applying

**that**supposed algorithm

**to**

**the**equation obtained from

**the**

__given__equation by replacing each unknown by

**the**sum

**of**

**the**squares

**of**four new unknowns

**.**

__Conversely__

**,**

**a**disease

**that**is easily transmitted but has

**a**

**short**duration might spread widely during 2002 but is likely

**to**have

**a**low prevalence at any

__given__point in 2003 ( due

**to**its

**short**duration ) but

**a**high incidence during 2002 ( as many people develop

**the**disease ).

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