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Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.

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## Some Related Sentences

Every and epimorphism

Every and algebraic

__Every__field has

**an**

__algebraic__extension which

**is**algebraically closed ( called its

__algebraic__closure ),

**but**proving

**this**

**in**general requires some form

**of**

**the**axiom

**of**choice

**.**

*

__Every__root**of**a monic polynomial whose coefficients are__algebraic__integers**is**itself**an**__algebraic__integer**.**__Every__

__algebraic__structure has its own notion

**of**homomorphism

**,**namely any function compatible with

**the**operation ( s ) defining

**the**structure

**.**

__Every__

__algebraic__curve C

**of**genus g ≥ 1

**is**associated with

**an**abelian variety J

**of**dimension g

**,**by means

**of**

**an**analytic map

**of**C into J

**.**

*

__Every__nonempty affine__algebraic__set may be written uniquely as a union**of**__algebraic__varieties ( where none**of****the**sets**in****the**decomposition are subsets**of**each other ).
*

__Every__holomorphic vector bundle on a projective variety**is**induced by a unique__algebraic__vector bundle**.**
*

__Every__real__algebraic__number field K**of**degree n contains a PV number**of**degree n**.**This number**is**a field generator**.**
*

__Every__substructure**is****the**union**of**its finitely generated substructures ; hence Sub ( A )**is****an**__algebraic__lattice**.**
Also

**,**a kind**of****converse**holds:__Every____algebraic__lattice**is**isomorphic to Sub ( A ) for some algebra A**.**
*

__Every__character value**is**a sum**of**n m < sup > th </ sup > roots**of**unity**,**where n**is****the**degree ( that**is****,****the**dimension**of****the**associated vector space )**of****the**representation with character χ and m**is****the**order**of**g**.**In particular**,**when F**is****the**field**of**complex numbers**,**every such character value**is****an**__algebraic__integer**.**
* Let K < sup > a </ sup > be

**an**__algebraic__closure**of**K containing L**.**__Every__embedding σ**of**L**in**K < sup > a </ sup > which restricts to**the**identity on K**,**satisfies σ ( L ) = L**.**In other words**,**σ**is****an**automorphism**of**L over K**.**__Every__

__algebraic__plane curve has a degree

**,**which can be defined

**,**

**in**case

**of**

**an**algebraically closed field

**,**as number

**of**intersections

**of**

**the**curve with a generic line

**.**

__Every__planar graph has

**an**

__algebraic__dual

**,**which

**is**

**in**general

**not**unique ( any dual defined by a plane embedding will do ).

Every and sense

__Every__gun that

**is**made

**,**every warship launched

**,**every rocket fired signifies

**,**

**in**

**the**final

__sense__

**,**a theft from those who hunger and are

**not**fed

**,**those who are cold and are

**not**clothed

**.**

__Every__morphism

**in**a concrete

**category**whose underlying function

**is**injective

**is**a monomorphism ;

**in**other words

**,**if morphisms are actually functions between sets

**,**then any morphism which

**is**a one-to-one function will necessarily be a monomorphism

**in**

**the**categorical

__sense__

**.**

'

__Every__one**of**those unfortunates during**the**process**of**existence should constantly__sense__and be cognizant**of****the**inevitability**of**his own death as well as**of****the**death**of**everyone upon whom his eyes or attention rests '.
(

__Every__diocese**is**a particular Church**,****but****not****an**autonomous one**in****the**__sense__**in**which**the**word**is**applied to these 22 Churches**.**
As

**the**Catholic Encyclopedia ( 1908 – 10 ) described his work "__Every__page**of**his writings reveals a wealth**of**strong common__sense__**,**clear perception**,**and a vein**of**wonderful and ever varying erudition**.**__Every__April

**,**one week

**is**set aside

**in**

**the**Greek community for Greek Week

**,**a series

**of**coed competitions that instill a

__sense__

**of**unity among

**the**houses

**,**while providing friendly competitiveness

**.**

__Every__language has a word expressing good

**in**

**the**

__sense__

**of**" having

**the**right or desirable quality " ( ἀρετή ) and bad

**in**

**the**

__sense__" undesirable ".

__Every__academician might use his favourite form

**of**Interlingua

**,**

**the**term being initially used

**in**a general

__sense__as a synonym for international language

**,**yet it soon began to be specially used to denote a reformed Latino sine flexione based on

**the**common rules

**the**academicians were reaching by frequent votings

**.**

*

__Every__Borel set B ⊆ R < sup > n </ sup >**is**μ-measurable**in****the**__sense__**of**Carathéodory's criterion: for every A ⊆ R < sup > n </ sup >,__Every__domain D can be embedded

**in**

**an**ω-complete domain completion ( called

**the**ω-completion or simply

**the**completion

**of**D ) that

**is**

**,**

**in**a precise

__sense__

**,**

**the**smallest ω-complete domain containing D

**.**The isolated elements

**of**completion are precisely

**the**isolated elements

**of**D

**,**

**but**

**in**general completion contains limit points that are

**not**found

**in**D

**.**completion

**is**uniquely determined up to isomorphism

**.**

__Every__( normal ) Boolean algebra with operators can be represented as a field

**of**sets on a relational structure

**in**

**the**

__sense__that it

**is**isomorphic to

**the**complex algebra corresponding to

**the**field

**.**

" The elaborate hypertext

**is**much like**the**book which Borges suggests to be**the**labyrinth**,**("__Every__one imagined two works ; to no one did it occur that**the**book and**the**maze were one and**the**same thing ...**the**confusion**of****the**novel suggested to me that it was**the**maze ")**in**a__sense__**of**how**the**site offers different approaches to how you may interpret**the**information provided**,**yet you're**not**trapped**in****the**dilemma**of**choosing one and eliminating others ; you may choose to unfold**all**possibilities**.**__Every__language

**is**mixed to some extent

**but**few languages are " mixed languages "

**in**

**the**specific

__sense__here

**.**

" Parker J

**.**Palmer wrote**,**"__Every__thoughtful adult I know**is**concerned that many American youth seem to lack a__sense__**of**purpose**in**their lives**.**
J

**.**D**.**Considine**of**Rolling Stone wrote**in****the**review**of**Bobby ( 1992 ), " As anyone who saw him swagger through**the**videos for ' My Prerogative ' and '__Every__Little Step ' can attest**,**Brown had a phenomenal ability to convey a__sense__**of**street toughness that was utterly without malice or menace**,**making him credible and likable ".
Faculty member Barbara Breitman says

**,**“__Every__spiritual tradition has within it**the**qualities**of**soul that people need to cultivate**in**their lives so that they can live according to a higher__sense__**of**purpose: generosity**,**patience**,**gratitude**,**truthfulness**.**
:"

__Every__gun that**is**made**,**every warship launched**,**every rocket fired**,**signifies**,****in****the**final__sense__**,**a theft from those who hunger and are**not**fed**,**those who are cold and**not**clothed**.**0.807 seconds.