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Topic: Monomorphism

Related Topics

Monic morphism

Epimorphism

Adjoint functors

Endomorphism ring

Preregular space

Abstract algebra

Subobject

Isomorphism

Category of metric spaces

Topological space

Kolmogorov space

Saunders Mac Lane

Complete space

Hausdorff space

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	Normal morphism - Wikipedia, the free encyclopedia
		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.
		In an abelian category, every monomorphism is the kernel of its cokernel, and every epimorphism is the cokernel of its kernel.
	en.wikipedia.org /wiki/Normal_morphism (292 words)

	Monomorphism - Wikipedia, the free encyclopedia
		The dual of a monomorphism is an epimorphism (i.e.
		An example of a monomorphism that is not injective arises in the category Div of divisible abelian groups and group homomorphisms between them.
		An extremal monomorphism is a monomorphism that has no epimorphism as a first factor, unless that epimorphism is an isomorphism.
	en.wikipedia.org /wiki/Monomorphism (442 words)

	Health & Wellness - Blood Analysis - The History Behind The Controversy
		Monomorphism blood analysis was discovered in the 1800s, and this is what Western or current medicine still teaches in medical institutions.
		Monomorphism is the cornerstone of Robert Koch’s (1843-1910) and Louis Pasteur’s (1822-1895) Germ Theory of Disease.
		Monomorphism verses Pleomorphism blood analysis continues to be opposed, because they blur the distinction between bacterium and virus, raising fundamental questions about the cause of illness.
	www.risingwomen.com /arcrowe27.htm (981 words)

	Monic and Epic Morphisms
		When a morphism is monic it probably implements a monomorphism, and when a morphism is epic it probably implements an epimorphism.
		This is not surprising; an isomorphism is both a monomorphism and an epimorphism.
		A monomorphism and an epimorphism is completely reversible, and the inverse function almost always obeys the rules of the category, creating an isomorphism.
	www.mathreference.com /cat,monic.html (770 words)

	REPEATED EVOLUTION OF SEXUAL COLOR DIMORPHISM IN PASSERINE BIRDS
		Using the parsimony method, 227 ancestral nodes were reconstructed as monomorphic, with 11 (4.8%) subsequent monomorphic-to-dimor- phic transitions, and 136 nodes were recon- structed as dimorphic, with 9 (6.6%) subsequent dimorphic-to-monomorphic transitions.
		However, com- parisons of dimorphic and monomorphic pop- ulations within a single species can be used to unequivocally identify monomorphic popula- tions as relatively dull (like the female of the dimorphic population) or bright (like the male of the dimorphic population).
		We suggest that this is a high number, and that the evolution of dimorphism from monomorphism (or its converse, mono- morphism from dimorphism) is not constrained greatly by an absence of genetic variation for dimorphism.
	elibrary.unm.edu /sora/Auk/v113n04/p0842-p0848.html (8115 words)

	Morphism (Site not responding. Last check: 2007-11-06)
		Monomorphisms in concrete categories are typically injective morphisms.
		Any morphism that is both an epimorphism and a split monomorphism, or both a monomorphism and a split epimorphism, must be an isomorphism.
		The terms isomorphism, epimorphism, monomorphism, endomorphism, and automorphism are all used in that specialized context as well.
	www.yotor.com /wiki/en/mo/Morphism.htm (791 words)

	Untitled Document (Site not responding. Last check: 2007-11-06)
		One hypothesis for monomorphism in cheetahs states that during the Pleistocene extinction, the cheetah experienced a population bottleneck (O’Brien et al.
		Years have been dedicated to assessing the extent of monomorphism and analyzing the possibilities of how the species became so depauperate in genetic variability.
		Researchers use the results from these tests to support the hypothesis that cheetahs are moving toward extinction as a result of genetic factors.
	www.beloit.edu /~biology/Sample_Paper.htm (2194 words)

	Implict parameters and monomorphism (Site not responding. Last check: 2007-11-06)
		Except, of course, for top level bindings which is where the monomorphism restriction is usually most noticable.
		> I would remove the monomorphism restriction, [...] This seems to be a pretty common sentiment but I don't see anyone pointing out that the monomorphism restriction is there for _two_ reasons: 1) The performance issues that are currently getting all the attention.
		This example comes from the H'98 report, section 4.5.5 "The Monomorphism Restriction".
	www.haskell.org /pipermail/haskell/2001-May/007127.html (187 words)

	[No title]
		X is a monomorphism, too, we need to define what it means for a morphism of an extended p-compact torus to a p-compact group to be a monomorphism.
		ss0(H)a monomorphism, and the Euler characteristic O(H=G) = ss0(H) : imss0(f).
		Thus g0 is both a rational isomorp* hism [7, 9.7] and a monomorphism*, hence [11, 3.7] [6, 4.7] an isomorphism.
	hopf.math.purdue.edu /Moller/normalizer.txt (3834 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The inclusion of the integers in the rationals is both an epimorphism and a monomorphism, but clearly not an isomorphism.
		[.snip.] >Or, in the category of all topological spaces and continuous >maps, a map f: X -> Y is a monomorphism iff it is an injection, >and it is an epimorphism iff it is a surjection.
		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)

	Restricting polymorphism (Site not responding. Last check: 2007-11-06)
		The monomorphism restriction prevents computations from being unexpectedly repeated to satisfy different overloadings.
		The monomorphism restriction has the added bonus of limiting certain types of ambiguity, but it comes with the cost of some subtle differences in the way Haskell types an expression.
		These curious subtleties are considered undesirable, and for this reason the monomorphism restriction is viewed as a provisional fix.
	www.cs.utexas.edu /users/emery/fp+oop=haskell/node13.html (261 words)

	[No title]
		Proposition (2.4.2) The natural morphism of a Spec of a local ring of a point into a prescheme is a monomorphism.
		Monomorphism means the same in both cases.) Proof: X x Y --> X' x Y'.
		G notes that it follows that monomorphisms are preserved by base change (+++ by the argument of (3.5.1)).
	math.stanford.edu /~vakil/ega1 (1799 words)

	Implict parameters and monomorphism (Site not responding. Last check: 2007-11-06)
		We noted the dire impact of the monomorphism restriction, and commented upon it.
		Again and again I have been forced to conclude, the only thing worse than having the monomorphism restriction is not having the monomorphism restriction.
		As a quick fix we should just pick one of A, B or C. Maybe A is the right one, prohibiting the problematical situation from arising at all.
	www.haskell.org /pipermail/haskell/2001-May/007130.html (318 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		In topological spaces, points are primordial and a monomorphism of points need not be a monomorphism of the attached frames (that is a surjection of the open set lattices).
		When it is, then ignoring the usual separation axiom, it is a subspace and thereby a kernel.
		Now a monomorphism must be injective on the points and surjective on the opens and is obviously a kernel.
	www.mta.ca /~cat-dist/catlist/1999/chu-abelian (664 words)

	NTU Info Centre: Abelian category (Site not responding. Last check: 2007-11-06)
		Finally, a preabelian category is abelian if every monomorphism and every epimorphism is normal.
		This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism.
		This epimorphism is called the coimage of f, while the monomorphism is called the image of f.
	www.nowtryus.com /article:Abelian_category (893 words)

	Institute of Mathematics of National Academy of Sciences of Armenia (Site not responding. Last check: 2007-11-06)
		Asatryan, Non-hereditary monomorphisms in categories of groups over general categories, pp.
		A non--hereditary monomorphism, in a group category $\Cal{G}\Cal{C}$ over a category $\Cal{C}$, is a monomorphism of $\Cal{G}\Cal{C}$ with a non-monic base morphism in $\Cal{C}$.
		The present article constructs typical examples of categories $\Cal{C}$ with non--hereditary monomorphisms in $\Cal{G}\Cal{C}$ and gives necessary and sufficient conditions for existence of non--hereditary monomorphisms.
	math.sci.am /Journal/2000_5.html (432 words)

	Archives of the Caml Mailing list: monomorphism is ... ? (Site not responding. Last check: 2007-11-06)
		Archives of the Caml Mailing list: monomorphism is...
		Next in thread: Pierre Weis: "Re: monomorphism is...
		This archive was generated by hypermail 2b29 : Sun Jan 02 2000 - 11:58:18 MET
	pauillac.inria.fr /caml/caml-list/0941.html (111 words)

	Properties of functions
		Proposition 3.1 A function is one-to-one if and only if it is a monomorphism.
		where e is an epimorphism and m is a monomorphism.
		Proposition 3.5 The composition of monomorphisms is a monomorphism.
	www.iwu.edu /~lstout/theoremlist/node8.html (148 words)

	MAS5307---Categorical stuff (Site not responding. Last check: 2007-11-06)
		CAT1: We have seen that a `monomorphism' in a category is a morphism f such that for all morphisms g, h which can be composed on the right of f, we have that fg=fh if and only if g=h.
		Also, we have seen that a set function is a monomorphism in the category Sets if and only if it is injective.
		Define similarly a notion of `epimorphism', so that a set function is an epimorphism in the category Sets if and only if it is surjective.
	www.math.fsu.edu /~aluffi/courses/2004-5/MAS5307/cats.html (172 words)

	[No title]
		I would like to know if it is a monomorphism.
		If G is not discrete I think there are examples when this compactification has a kernel.
		If G is not > discrete I think there are examples when this compactification has a > kernel.
	www.math.niu.edu /~rusin/known-math/99/compactification_grp (1216 words)

	Paramārtha and Modern Constructivists on Mysticism: Epistemological Monomorphism Versus Duomorphism - Questia Online ... (Site not responding. Last check: 2007-11-06)
		Paramārtha and modern constructivists on mysticism: Epistemological monomorphism versus duomorphism
		One of the axioms of what may be called the received view in the postWittgensteinian humanities and social sciences is that my experience of something, say a door, is highly shaped and conditioned by my concepts, expectations, beliefs, and so forth about doors.
		Choose a subscription plan to save tons of time, stress and hassle, and do better research, faster.
	www.questia.com /PM.qst?a=o&d=95137698 (509 words)

	HacWrite - 40 Comments on Haskell and other language design issues
		Through experiences with other languages, we have also realised that some languages features not currently supported by Haskell would be useful to have.
		One of the most annoying features of Haskell, when trying to program in a combinatorial style, is the monomorphism restriction.
		It means that a definition that is not syntactically a function is not allowed to be overloaded, unless an explicit type signature is provided.
	www.cs.chalmers.se /~hallgren/Thesis/haskell-comments.html (1024 words)

	Polymorphism and Monomorphism in Martin-Lof's Type Theory - Salvesen (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		In the monomorphic version, MTS, expressions contain explicit type information and are uniquely typed, while in the polymorphic version, ITT, expressions do not contain this information and may be given a multiple of types.
		The comparison shows that we cannot understand the polymorphic system just as a simplification of the monomorphic by stripping o# type information.
		3 The Monomorphic Theory of Sets (MTS) This theory was defined by Martin Lof [ML75] as a system for formalising intuitionistic...
	citeseer.ist.psu.edu /salvesen88polymorphism.html (377 words)

	ACTA Sep1999: False Negative Cytologic Diagnosis of Breast Carcinoma (Site not responding. Last check: 2007-11-06)
		Conclusion: The presence of associated fibrocystic disease may be a misleading factor since it may mask a malignancy.
		Hypocellularity and relatively nuclear monomorphism were the most common reasons for failure to diagnose malignant breast lesions.
		Careful attention should be paid to extreme nuclear monomorphism and absence of naked bipolar cells.
	www.acta-cytol.com /Abs/ACTA741.htm (198 words)

	"NATURALLY...YOU!", Homeopathic Solutions--Is Homeopathy Scientific? (Site not responding. Last check: 2007-11-06)
		Bechamp said that microorganisms actually are the result of a change in the form of ubiquitous and normally innocuous microzymas which live in the body in a different forms which correspond to a changes in the health and terrain of the individual (pleomorphism).
		Pasteur said that the microorganisms found in a sick patient have come into the economy from the outside and have caused the illness and only have one form (monomorphism).
		Well, we all know which theory has become the dominant one in Allopathic Medicine; however, as a Classical Homeopath with over fifteen years of experience, I believe Bechamp to be correct.
	www.onlinehomeopath.com /science.shtml (3990 words)

	High MHC diversity maintained by balancing selection in an otherwise genetically monomorphic mammal -- Aguilar et al. ...
		High MHC diversity maintained by balancing selection in an otherwise genetically monomorphic mammal -- Aguilar et al.
		kin and non-kin in territorial encounters (13), monomorphism
		DQB locus was monomorphic in the San Nicolas population.
	www.pnas.org /cgi/content/full/101/10/3490 (3467 words)

	Polymorphism
		Before a fuller description of polymorphism it might help to provide a justification.
		Polymorphism can be seen as an attempt to overcome the inflexibility of type monomorphism and still retain the advantages of static type checking.
		A monomorphic type system is one where procedures or functions can be applied to only one type.
	homepages.feis.herts.ac.uk /~msc_fl/fl-node58.html (323 words)

	An Axiomatic Description of a Duality for Modules - Krause (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		We shall identify the category of left-modules with Mod(op).
		Recall that a-module M is pure-injective if every pure monomorphism starting in M splits.
		N\Omega X is a monomorphism for every X in mod(op).
	citeseer.ist.psu.edu /krause97axiomatic.html (361 words)

	categorytheory.html
		is called a monomorphism if for any object
		The Category of Sets - onto is equivalent to epimorphism, and one to one is equivalent to monomorphism.
		One can find examples of monomorphisms that are not one to one as Set maps.
	www.umsl.edu /~siegel/SetTheoryandTopology/categorytheory.html (67 words)

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