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Topic: Normal morphism

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	Automorphism - Wikipedia, the free encyclopedia
		a morphism from an object to itself) which is also an isomorphism (in the categorical sense of the word).
		In the context of abstract algebra, for example, a mathematical object is an algebraic structure such as a group, ring, or vector space.
		Identity: the identity is the identity morphism from an object to itself which exists by definition.
	en.wikipedia.org /wiki/Automorphism (898 words)

	Morphism (Site not responding. Last check: 2007-10-20)
		The abstract study of morphisms and the spaces (or objects) on which they are defined forms a branch of mathematics called category theory.
		Despite the abstract nature of morphisms, most people's intution about them (and indeed much of the terminology) comes from the case of the so-called concrete categories where the objects are simply sets with some additional structure and morphisms are functions preserving this structure.
		Any morphism that is both an epimorphism and a split monomorphism, or both a monomorphism and a split epimorphism, must be an isomorphism.
	www.yotor.com /wiki/en/mo/Morphism.htm (791 words)

	Normal (Site not responding. Last check: 2007-10-20)
		In algebra (in particular, group theory): a normal subgroup is a subgroup that is invariant under conjugation.
		In functional analysis: a normal operator is a linear operator on a Hilbert space that commutes with its adjoint.
		In category theory: a normal morphism is a morphism that arises as the kernel or cokernel of some other morphisms.
	www.theezine.net /n/normal.html (330 words)

	[No title]
		Q) is the normal closure NQ (M) of M in Q. Thus the induced crossed m* odule construction replaces this normal* closure by a bigger group on which Q acts, an* *d which has a universal property not usually enjoyed by NQ (M).
		Q, * in the case P and M are normal* in Q. In section 2 we use the presentation of induced crossed modules given in [3,* * 7] to describe the crossed module induced by the normal inclusion in terms of the coproduct o* *f crossed P -modules discussed in [12, 1].
		We now assume that P is a normal subgroup of Q, and show in Theorem 2.2 that* * the coproduct of crossed P -modules may be used to give a presentation of induced c* *rossed P - modules analogous to known presentations of induced modules.
	hopf.math.purdue.edu /BrownR-Wensley/ind-nrm4.txt (3810 words)

	Normal morphism (Site not responding. Last check: 2007-10-20)
		In category theory and its applications to mathematics, a normal monomorphism or normal epimorphism is a particularly well-behaved type of morphism.
		A normal category is a category in which morphisms are normal, whenever reasonable.
		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.
	www.sciencedaily.com /encyclopedia/normal_morphism (330 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		We associate a morphism $(B, W, Q)\to (B, W, Q')$ of space germs induced by the identity homomorphisms of the quotient field of $B$.
		The underlying morphism $(B,W)\to(B', W')$ of the associated morphism $(B,W,Q)\to(B', W',Q')$ is called the associated morphism with the elementary monoidal transform $(B', W')$ of $(B, W)$.
		The underlying morphism $(B,W)\to(B', W')$ of the associated morphism $(B,W,Q)\to(B', W',Q')$ is called the associated morphism with the IAMT $(B', W')$ of $(B, W)$.
	home.imf.au.dk /esn/preprints/139 (8944 words)

	Fibrewise General Topology: A Brief Outlook by David Buhagiar
		For example, there is no analogue to Urysohn's Lemma for maps and so normality and functional normality do not coincide and as a consequence, there exist two theories of compactifications, one for Hausdorff compactifications and one for Tychonoff compactifications.
		Collectionwise normal maps were defined by the author [8] and enabled the definition of metrizable type maps, giving a satisfactory fibrewise version of the theory of metrizable spaces.
		It is not difficult to see that this definition of a morphism in MAP satisfies the necessary axioms that morphisms should satisfy in any category (see, for example, [21]).
	at.yorku.ca /t/a/i/c/34.htm (1505 words)

	GAP Manual: 73.127 About induced constructions
		A morphism of crossed modules (sigma, rho) : {cal X}_1 to {cal X}_2 factors uniquely through an induced crossed module rho_{ast} {cal X}_1 = (delta : rho_{ast} S_1 to R_2).
		Data for the cases of algebraic interest is provided by a conjugation crossed module {cal X} = (partial : S to R) and a homomorphism iota from R to a third group Q.
		When iota is neither a surjection nor an inclusion, iota is written as the composite of the surjection onto the image and the inclusion of the image in Q, and then the composite induced crossed module is constructed.
	www-groups.dcs.st-and.ac.uk /gap/Gap3/Manual3/C073S127.htm (477 words)

	Reports of the Mathematical Institute Leiden (Site not responding. Last check: 2007-10-20)
		We show that the image of a commutative monotone sequentially complete C-algebra, under a sequentially normal* morphism, is again a monotone sequentially complete C-algebra, and also a monotone sequentially closed C-subalgebra.
		As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed.
		In the case of a unital representation of C(X) in a separable Hilbert space, where X is a compact Hausdorff space, this implies that the von Neumann algebra generated by the image of C(X) is the image of the Baire functions on X under the extension of the representation to the bounded Borel functions.
	www.math.leidenuniv.nl /reports/2003-16.shtml (122 words)

	Encyclopedia article on Topological space [EncycloZine] (Site not responding. Last check: 2007-10-20)
		The category of topological spaces, Top, with topological spaces as objects and continuous functions as morphisms is one of the fundamental categories in mathematics.
		The attempt to classify the objects of this category by invariants has motivated and generated entire areas of research, such as homotopy theory, homology theory, and K-theory, to name just a few.
		A space is normal if any two disjoint closed sets have disjoint neighbourhoods.
	encyclozine.com /Topological_space (2350 words)

	On the Practical Value of Different Definitional Translations to Normal Form - Egly, Rath (ResearchIndex)
		In this paper, we compare different normal form translations from a practical point of view.
		The usual translation of a closed firstorder formula to a disjunctive normal form has severe drawbacks, namely the disruption of the formula's structure and an exponential worst case complexity.
		Another example for input transformation is the logic morphism for propositional intuitionistic logic [Kor96] which will be...
	citeseer.ist.psu.edu /egly96practical.html (715 words)

	GAP Manual: 73 XMOD (Site not responding. Last check: 2007-10-20)
		R [,S] This construction returns the crossed module whose source S is a normal subgroup of the range R, the boundary is the inclusion map, the group of automorphisms is the inner automorphism group of S, and the action maps an element of r ∈ R to conjugation of S by r.
		They also ensure that the inclusion morphism of a normal sub-crossed module forms a conjugation crossed square, analogous to the construction of a conjugation crossed module.
		This function takes pairs of normal subgroups from the source and range of C and constructs a normal sub-cat1-group whenever the axioms are satisfied.
	www.math.jussieu.fr /~jmichel/htm/CHAP073.htm (7566 words)

	Gaston Nassens; Pleo-morphism, Acid Base, Metabolic Acidosis and Base Powder (Site not responding. Last check: 2007-10-20)
		Furthermore, Naessens has discovered that Somatids, the process of pleomorphism, living in healthy human bodies go through a normal, recurring 3-stage pleomorphic sub cellular developmental cycle, and that each stage of this recurring cycle is directly related to healthy cellular development, acid base and growth.
		These three stages are listed as 1, 2, 3, in the diagram below and correspond exactly to what we have been talking about, the only difference beings the names assigned to these forms.
		The normal 3-stages he represents here are of course the same as the PROTIT, FREE CHONDRIT, and the LOWER VALENCED CHONDRIT FORMS of Enderlein.
	www.euroamericanhealth.com /gaston.html (1062 words)

	9.1 Hyperelliptic curves (Site not responding. Last check: 2007-10-20)
		; also known as the ``rational normal curve of degree d''; this is given as the locus of
		It is clear that the vertex v does not lie on T so that projection gives a morphism on T which lands in the rational normal curve of degree d.
		The variety T is called a hyperelliptic curve, the involution is called the hyperelliptic involution and the morphism
	www.imsc.ernet.in /~kapil/crypto/notes/node48.html (510 words)

	Uniqueness of Normal Proofs in $\{\rightarrow, \wedge\}$-Fragment of NJ (ResearchIndex)
		Abstract: It is known that in f!;g-fragment of the natural deduction system of intuitionistic propositional logic NJ balanced formulas have unique fij-normal proofs.
		2 A coherence thorem for canonical morphism in cartesian close..
		Unique Normal Proof Property for Implicational Minimal Formulas in..
	citeseer.ist.psu.edu /491673.html (301 words)

	Concurrency Abstracts (Site not responding. Last check: 2007-10-20)
		We show that a normal form exists for every closed term of the algebra and establish soundness of our axiom system with respect to a schedule semantics, as well as completeness for efficient processes.
		Uncertainty arises when we define a measurement to be a morphism and notice that increasing structure in the observed object reduces clarity of observation.
		Its algebraic structure is essentially that of linear logic, with its morphisms being consequence-preserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language.
	boole.stanford.edu /abstracts.html (9620 words)

	PlanetMath:
		affine morphism (in finite morphism) owned by rmilson
		alternating group is a normal subgroup of the symmetric group owned by mathcam
		average order (in normal order) owned by saforres
	planetmath.org /encyclopedia/A (1757 words)

	[No title]
		# $Source: /u/maple/research/lib/algcurves/src/RCS/ratpar,v $ # $Notify: mvanhoei@daisy.uwaterloo.ca $ # #--> ratpar: Compute a rational bijective morphism from a conic or a line # to a given curve f with genus 0.
		This is done by searching an odd point on C2, # and for this we search for odd regular points on C. If this fails # then we compute the inverse morphism, i.e.
		1 then return procname(f,x,y, numer(g_normal(a/evala(Norm(x-r)))),ext) fi; [r,subs(solve({v[1][1]},{y}),y),1] end: # Let g be a bijective morphism from C to C2.
	www.math.fsu.edu /~hoeij/lib/algcurves/src/ratpar (2279 words)

	Theory Subgroup (Isabelle99-1: October 2000) (Site not responding. Last check: 2007-10-20)
		theory Subgroup = OGroup + Elementary + Morphism:
		(* Pierre Castéran et [JSA] ) header { Groups as first-class object } theory Subgroup = OGroup + Elementary + Morphism* :; subsection {* the subgroup preorder } text { Let G be a group.
		(normal H G) ; x:(domain G) ; y:(domain H) ] ==>((law G) x ((law G) y (sym_fun G x)) :(domain H))" proof(unfold normal_def,blast) qed lemma sub_H_group[simp]:"subgroup H G==>group H" proof(unfold subgroup_def,blast) qed subsection {* elementary rules *} lemma exist_x_in_sub[simp] : "subgroup H G ==> EX x.
	www.labri.u-bordeaux.fr /Perso/~bouquet/Html/Subgroup.html (326 words)

	GAP Manual: 73.41 Kernel of a crossed module morphism (Site not responding. Last check: 2007-10-20)
		GAP Manual: 73.41 Kernel of a crossed module morphism
		: X to Y of crossed modules is the normal sub-crossed module of X whose source is the kernel of
		An appropriate name for the kernel is chosen automatically.
	www-groups.dcs.st-and.ac.uk /gap/Gap3/Manual3/C073S041.htm (38 words)

	Ekedahl: Canonical models of surfaces of general type in positive characteristic
		GIRAUD, Forme normale d'une fonction sur une surface de caractéristique positive, Bull.
		MIYAOKA, Deformations of a morphism along a foliation, Proceedings of Symposia in Pure Math., 46, Part 1 (
		TANGO, On morphisms from projective space Pn, J. Math.
	www.numdam.org /numdam-bin/recherche?h=nc&id=PMIHES_1988__67__97_0&format=complete (233 words)

	Resolution of Singularities (Site not responding. Last check: 2007-10-20)
		The objective of the program of resolution of singularities is to find a birational projective morphism
		A much sharper version of the following conjecture was proved by Hironaka in his celebrated paper [
		In non-zero characteristic this case is known to be difficult due the the fact that the fundamental group of the affine line being non-trivial.
	www.imsc.ernet.in /~kapil/work/node11.html (184 words)

	Morphism, 16 June 2001
		I'm going to do at least one other Minnesota-local dark fantasy story, but I really need to get into the Saint Paul Winter Carnival before I can do it.
		That one seems almost normal compared to the butterheads.
		I went to the post office yesterday to send rejected fantasy novels to a certain sister-in-law who shall remain nameless.
	www.marissalingen.com /061601.html (818 words)

	ICTP Preprints Abstract List
		Finally, we give a clear structure of singularities of the solution for a system with the form of conservation laws.
		ABSTRACT: This paper solves the global moduli problem for regular holonomic $\cal D$-modules with normal crossing singularities on a nonsingular complex projective variety.
		ABSTRACT: Let $G$ be any compact but not necessarily connected Lie group, and let $M$ be any connected paracompact manifold.
	www.ictp.trieste.it /www_users/math/1997_preprints.html (1327 words)

	biblio_hoffer
		Altschul R and Hoffer A. The effect of nicotinic acid upon serum cholesterol and upon basal metabolic rate of young normal adults.
		Hoffer A and Osmond H. The adrenochrome model and schizophrenia.
		Hoffer A, Foster, HD: Schizophrenia and cancer: the adrenochrome balanced morphism, Med Hypotheses.
	www.doctoryourself.com /biblio_hoffer.html (3694 words)

	CTO : Glossary
		Equality - The term for a relation among objects within a given context determining their comparitive identity - whether they are the same or different from a given perspective
		Fault-tolerant - The term for the ability of a system to continue normal operation despite the presence of hardware or software faults
		Morphism - A term related to category theory describing a map between two objects in an abstract category
	cliki.tunes.org /Glossary (4571 words)

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