
	Where results make sense

Topic: Epimorphism

Related Topics

Monomorphism

Endomorphism ring

Adjoint functors

Category of metric spaces

Isomorphism

Preregular space

Subobject

Topological space

Saunders Mac Lane

Complete space

Kolmogorov space

Curve

Hausdorff space

Monic morphism

	Epimorphism - Wikipedia, the free encyclopedia
		Epimorphisms are analogues of surjective functions, but they are not exactly the same.
		The dual of an epimorphism is a monomorphism (i.e.
		An extremal epimorphism is an epimorphism that has no monomorphism as a second factor, unless that monomorphism is an isomorphism.
	en.wikipedia.org /wiki/Epimorphism (1548 words)

	Epimorphism - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		In the context of abstract algebra or universal algebra, an epimorphism is simply a surjective homomorphism.
		In the category of monoids, Mon, the inclusion function N → Z is a non-surjective monoid homomorphism, and hence not an algebraic epimorphism.
		It is, however, a epimorphism in the categorical sense.
	www.encyclopedia-online.info /Epic_morphism (206 words)

	Normal morphism
		In category theory and its applications to mathematics, a normal monomorphism or normal epimorphism is a particularly well-behaved type of morphism.
		In that case, we say that a monomorphism is normal if it is the kernel of some morphism, and an epimorphism is normal (or conormal) if it is the cokernel[?] of some morphism.
		The category of abelian groups is the fundamental example of an abelian category, and accordingly every subgroup of an abelian group is a normal subgroup.
	www.ebroadcast.com.au /lookup/encyclopedia/bi/Binormality.html (253 words)

	Five lemma
		The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an epimorphism, and q is a monomorphism, then n is also an isomorphism.
		To perform diagram chasing, we assume that we are in a category of modules over some ring, so that we may speak of elements of the objects in the diagram and think of the morphisms of the diagram as functions (in fact, homomorphisms) acting on those elements.
		Then a morphism is a monomorphism if and only if it is injective, and it is an epimorphism iff it is surjective.
	www.ebroadcast.com.au /lookup/encyclopedia/fi/Five_lemma.html (606 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-07)
		In the categories of sets, vector spaces, groups, and Abelian groups, the epimorphisms are precisely the surjective mappings, i.e.
		However, in the categories of topological spaces or associative rings there are non-surjective epimorphisms (that is, mappings that are not "onto" ).
		The concept of an epimorphism is dual to that of a monomorphism.
	eom.springer.de /e/e035890.htm (179 words)

	Epimorphism (Site not responding. Last check: 2007-11-07)
		In the category of monoids Mon the inclusion function N → Z is a non-surjective monoid homomorphism and not an algebraic epimorphism.
		In the category of rings Ring the inclusion map Z → Q is a categorical epimorphism but not algebraic one.
		In general algebraic epimorphisms are always categorical but not vice-versa.
	www.freeglossary.com /Epimorphism (170 words)

	Monomorphism Encyclopedia Article @ Genetically.org (Site not responding. Last check: 2007-11-07)
		The companion terms monomorphism and epimorphism were originally introduced by Bourbaki; Bourbaki uses monomorphism as shorthand for an injective function.
		While this is not exactly true for monic maps, it is very close, so this has caused little trouble, unlike the case of epimorphisms.
		Saunders Mac Lane attempted to make a distinction between what he called monomorphisms, which were maps in a concrete category whose underlying maps of sets were injective, and monic maps, which are monomorphisms in the categorical sense of the word.
	www.genetically.org /encyclopedia/Monomorphism (628 words)

	For a mapping F to be a homomorphism, it must be true that F(x o y) = F(x) * F(y) for the given operations o and *
		For a mapping F to be an epimorphism, F must be a homomorphism that is surjective (onto).
		To check whether or not F is an epimorphism, we want to check whether or not the F represents a mapping that is surjective (onto).
		Thus the mapping F is not an epimorphism as it is not surjective (onto).
	students.uww.edu /muellerbt15/Homomorphisms.htm (608 words)

	Epimorphisms (Site not responding. Last check: 2007-11-07)
		Although it is true in the category of all Groups, it is false in other common categories of algebras, such as the category of semigroups (the embedding on the natural numbers into the integers is a non-surjective epimorphism), and the category of rings (the embedding of the integers into the rationals is a nonsurjective epimorphism).
		One wants to obtain a description of which maps are epimorphisms, whenever possible; for example, in the category of Hausdorff spaces, a morphism is an epimorphism if and only if the image is dense (in the usual topological sense).
		And also, there are a number of categorical constructions and concepts which are restricted to epimorphisms, and although they may be uninteresting when the epimorphism is surjective, they become rather more important when there are nonsurjective ones (an example of this is the notion of a 'projective').
	math.berkeley.edu /~magidin/research/epimorphisms.html (507 words)

	EPIMORPHISM (Site not responding. Last check: 2007-11-07)
		В общем, алгебреические epimorphisms находятся всегда категорически одни но vice-versa.
		Extremal epimorphism будет epimorphism не имеет никакую мономорфность как второй фактор, если той мономорфностью не быть однокачественность.
		It is licensed under the GNU free documentation license.
	www.faktoru.com /wiki/ru/ep/Epimorphism.htm (126 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Subject: Re: Surjectivity of epimorphisms of groups Date: Tue, 07 Mar 2000 12:25:33 -0500 Newsgroups: sci.math Summary: [missing] Arturo Magidin wrote: > [snip] > > In the case of objects with underlying sets, it is easy to show that > every surjective morphism is an epimorphism, adn every injective > morphism is an epimorphism.
		The inclusion of the integers in the rationals is both an epimorphism and a monomorphism, but clearly not an isomorphism.
		If the original map is a nonsurjective epimorphism, then the immersion from this factorization will be an epimorphism and an injection, hence a monomorphism, but not an isomorphism.
	www.math.niu.edu /~rusin/known-math/00_incoming/epimorphism (584 words)

	Epimorphism - the free encyclopedia (Site not responding. Last check: 2007-11-07)
		inclusion function N → Z is a non-surjective monoid homomorphism, and hence not an algebraic epimorphism.
		rings, Ring, the inclusion map Z → Q is a categorical epimorphism but not an algebraic one.
		An extremal epimorphism is an epimorphism that has no monomorphism as a second factor, unless that monomorphism is an
	www.the-free-web-encyclopedia.com /default.asp?t=Epimorphism (172 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-11-07)
		In category theory an epimorphism (also called an epic morphism or an epi) is a morphism f : X → Y which is "right-cancellable" in the following sense:
		To prove that every epimorphism in Top is surjective, we proceed exactly as in Set, giving the indiscrete topology which ensures that all considered maps are continuous.
		As for most concepts in category theory, epimorphisms are preserved under equivalences of categories: given an equivalence F : C → D, then a morphism f is an epimorphism in the category C if and only if F(f) is an epimorphism in D.
	www.hostingciamca.com /index.php?title=Epimorphism (1571 words)

	More general classes (Site not responding. Last check: 2007-11-07)
		Then any totally variant proper subgroup is epimorphically embedded into a finite nonabelian simple group in the variety it generates.
		Fortunately, in the case of nonsurjective epimorphisms, the result above is powerful enough to reduce the problem to the indecomposable varieties.
		I do have two partial results in that direction: if the epimorphism is into a finite nonabelian simple group G, then for any Q other than the variety of all groups NQ will have a nonsurjective epimorphism into a finite group.
	math.berkeley.edu /~magidin/research/moregen.html (857 words)

	-morphism glossary
		For example, in the category of =monoids, the inclusion of N into Z is an epimorphism (and =monomorphism) and in the category of rings, so is the inclusion Z into =Q. In non-algebraic situations, monomorphisms might not be injective, =although I don't have a simple example off-hand.
		For example, in the category of monoids, the inclusion of N into Z is an epimorphism (and monomorphism) and in the category of rings, so is the inclusion Z into Q.
		While monomorphism and epimorphism are categorical terms and probably should not be even mentioned till later on.
	www.forum-one.org /new-5413871-4346.html (1063 words)

	Epimorphism (Site not responding. Last check: 2007-11-07)
		In the context of abstract algebra or universal algebra, an epimorphism is simply an onto or surjective homomorphism.
		In category theory an epimorphism (also called an epic morphism or an epi) is a morphism f : X → Y such that
		(Indeed, any map from a commutative ring R to one of its localizations is an epimorphism.) To see this, note that any ring homomorphism on Q is determined entirely by its action on Z, similar to the previous example.
	www.reboom.com /article/Epimorphism.html (547 words)

	Monomorphism - ExampleProblems.com
		The use of the words monomorphism and epimorphism is somewhat unsettled.
		Mac Lane attempted to restore its original meanings by using the terms monic morphism or mono to refer to the category-theoretic concept, but this distinction has not caught on.
		However, whereas the difference is more notable in the case of epimorphisms, in "most" naturally occurring categories of algebras the categorical and algebraic meaning coincide because in any concrete category with a free object on a one element set the categorical monomorphisms are all one-to-one.
	www.exampleproblems.com /wiki/index.php/Monomorphism (426 words)

	PlanetMath: types of homomorphisms (Site not responding. Last check: 2007-11-07)
		Sometimes the term "epimorphism" is used as a synonym for "epic" -- in cases such as the term "ring epimorphism", this usage can lead to ambiguity, so one needs to check the author's usage.
		If a homomorphism has an inverse, then we say that it is an isomorphism.
		Cross-references: collection, Endomorphism, codomain, domain, bijective function, isomorphism, ring epimorphism, term, surjective, monic, injective function, properties, module, ring homomorphisms, similar, inverses, identity element, operator, binary, groups, category, information, maps, category theory, functions, relations, generated by, structures, algebraic structures
	planetmath.org /encyclopedia/Epimorphism3.html (398 words)

	Morphism
		Epimorphism s jednostranný inverzní je nazýván epimorphism rozkolu.
		Jestliže f je oba epimorphism a monomorfismus, pak f je bimorphism.
		Nicméně, nějaký morphism, který je jak epimorphism tak sekce, nebo oba monomorfismus a odvolání, muset být izomorfismus.
	wikipedia.infostar.cz /m/mo/morphism_1.html (329 words)

	News \| Gainesville.com \| The Gainesville Sun \| Gainesville, Fla. (Site not responding. Last check: 2007-11-07)
		This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism.
		Note that the enriched structure on hom-sets is a consequence of the three axioms of the first definition.
		This epimorphism is called the coimage of f, while the monomorphism is called the image of f.
	www.gainesville.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=abelian_category (982 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-07)
		A morphism having the characteristic property of the natural mapping of a group onto a quotient group or of a ring onto a quotient ring.
		The cokernel of any morphism is a normal epimorphism.
		The concept of a normal epimorphism is dual to that of a normal monomorphism.
	eom.springer.de /N/n067480.htm (120 words)

Try your search on: Qwika (all wikis)