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Page "Epimorphism" ¶ 4
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Every and epimorphism
Every retraction is an epimorphism, and every section is a monomorphism.
Every section is a monomorphism, and every retraction is an epimorphism.
Every morphism in a concrete category whose underlying function is surjective is an epimorphism.
* Every coequalizer is an epimorphism.
Every extremal epimorphism is regular.

Every and algebraic
** Every field has an algebraic closure.
Every root of a polynomial equation whose coefficients are algebraic numbers is again 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 field has an algebraic closure, and it is unique up to an isomorphism that fixes F.
* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.
* Every ( biregular ) algebraic automorphism of a projective space is projective linear.
* Every algebraic extension of k is separable.
* 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.
* Every finite poset is directed complete and algebraic.
* 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 existentially closed group ( in the model theoretic sense ) is divisible.
Every noun has a grammatically-correct diminutive form, regardless of the sense it makes.
* 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.
Showrunner Al Jean has said in an interview that " Every other place has had a good sense of humor.
" 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.
* Every element of S has a unique inverse, in the above sense.
" 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 ".
* " Every great artist has the sense of provocation.
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.

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