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Topic: Commutative diagram

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	PlanetMath: commutative diagram
		Usually diagrams are denoted by drawing the corresponding graph and labeling its vertices (respectively edges) with their images under
		Often (as in the previous example) the vertices themselves are not drawn since their position can be deduced by the position of their labels.
		This is version 9 of commutative diagram, born on 2003-02-02, modified 2006-10-15.
	planetmath.org /encyclopedia/CommutativeDiagram.html (139 words)

	neverendingbooks
		Next, we can associate to this special polygon a cuboid tree diagram by considering all even and odd vertices on the boundary (which are tinted red, respectively blue) together with all odd vertices in the interior of the special polygon.
		If we connect these vertices with the geodesics in the polygon we get a cuboid tree diagram.
		The obtained cuboid tree diagram is depicted on the right below.
	www.neverendingbooks.org (1192 words)

	Highbeam Encyclopedia - Search Results for commutative
		commutative law Rule of combination in mathematics; it requires that an operation on two terms is independent of the order of the terms.
		Addition and multiplication of numbers is commutative, since a + b = b + a and ab = ba.
		A commutative ring is one in which the...
	www.encyclopedia.com /SearchResults.aspx?Q=commutative (734 words)

	Commutative Diagrams
		Within the context of a category, a diagram is a digraph with objects as vertices and morphisms as edges.
		A commutative diagram is a diagram that exhibits path independence.
		In other words, the entire rectangle commutes, and wx,yz is a valid morphism from f to h.
	www.mathreference.com /cat,cdiag.html (514 words)

	Talk:Commutative diagram - Biocrawler (Site not responding. Last check: )
		This could serve to illustrate the last point: if all the "small" squares and triangles commute, then the whole diagram is automatically commutative.
		They say something about function composition, which is, after all, not commutative.
		The word "commutes" here is not being used in the sense of algebra; instead, it refers to a certain property of a diagram: any two composites of arrows with the same source and target in the diagram are equal.
	www.biocrawler.com /encyclopedia/Talk:Commutative_diagram (346 words)

	[No title]
		We use the notations and resul* ts of [18, xx15, 16], where the structure of cofibrant commutative* orthogonal ring sp* ectra is analyzed and the precisely analogous proof comparing commutative* symmetric ring spectra and commutative orthogonal ring spectrum is given.
		The case of commutative R-algebras follows from the previous proof since a cofibrant commutative R-algebra is cofibrant as a commutative orthogona* *l_ ring spectrum.
		X __g__//Y: (i)If the diagram is a pushout in which i is an h-cofibration and f is a ss- isomorphism, then g is a ss-isomorphism.
	hopf.math.purdue.edu /Mandell-May/MMM2.txt (21843 words)

	2- and 3-D Software Modeling
		Constraint diagrams is a visual technique, which was introduced recently for specification of the software and other large and complex systems.
		The intuitiveness of the constraint diagram language comes from it being a natural generalization of the following classical notations, which are part of standard mathematical education.
		Commutative Diagrams: a notation used in mathematics to describe properties of morphisms among mathematical structures.
	www.cs.technion.ac.il /Labs/ssdl/research/cdeditor/index.html (347 words)

	Commutative diagram - InformationBlast
		In mathematics, especially the many applications of category theory, a commutative diagram is a diagram of objects and morphisms such that, when picking two objects, one can follow any path through the diagram and obtain the same result by composition.
		For example, the first isomorphism theorem is a commutative triangle as follows:
		Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subdiagram is commutative.
	www.informationblast.com /Commutative_diagram.html (115 words)

	LaTeX Environments
		Sometimes a commutative diagram is triangular in which case we typeset a square diagram and use @= to indicate equality.
		Commutative diagrams do not have to have the same number of row as columns but they are on a rectangular grid.
		The label must be put at the end of the caption and the figure may be cross-referenced in the usual way with the \label and \ref commands..
	www.math.cmu.edu /~fabbri/latex/environ.htm (1447 words)

	[No title]
		The diagram is natural with respect to automorphisms of C. By definition, `C 2 A(C) Z Q corresponds to the idempotent (ffiCD)D in the lower left-hand corner.
		K0(R) _______//HH0Z(R) commutes, the upper horizontal map is an isomorphism and both vertical arrows a* *re injective.
		HH nZ S-1OF [G] _______________//HHnZ(F G) commutes, where the vertical maps are induced by the, up to G-homotopy, unique G-maps or are given by the trace maps; the horizontal arrows are induced by the inclusion of rings S-1OF F.
	hopf.math.purdue.edu /Lueck-Reich/lueckreich0805.txt (6376 words)

	Guidelines for Graphics in MathML 2
		Since the diagrams are about mathematical objects, they can contain mathematical formulae, and since diagrams are sometimes used to communicate mathemtatical objects they can occur inside mathematical formulae.
		The left diagram is a commutative diagrams, such diagrams are used in mathematics to visualize and argue about complex configurations of sets and mappings.
		Even though the use of diagrams or images inside of mathematical formulae is relatively rare in published mathematics (an exception seems to be slide presentations or other educational material), such cases do exist, e.g.
	www.w3.org /Math/Documents/Notes/graphics.xml (1841 words)

	Commutative Diagrams in TeX (Site not responding. Last check: )
		This is a macro package for drawing so-called "commutative" diagrams in category theory and related subjects.
		The pre-1992 pure DVI code in the diagrams package was a useful tool in its day, and I still try to make most of my diagrams work with it.
		The package makes two "passes" when constructing each diagram: one in which it constructs a "matrix" from the data that you type, and a second in which it takes this matrix apart and stretches each of the arrows to meet its endpoints.
	www.cs.man.ac.uk /~pt/diagrams (1701 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		A diagram is a simplified and structured visual representation of concepts, ideas, constructions, relations, statistical data, anatomy etc used in all aspects of human activities to visualize and clarify the topic.
		Sankey diagram - represents material, energy or cost flows with quantity proportional arrows in a process network.
		Sentence diagram -- represents the grammatical structure of a natural language sentence.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=diagram (207 words)

	[No title]
		Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists.
		Let Ar C be the category of morphisms in C. It is a diagram category, where the index category has two objects and a unique map between them.
		Suppose given two maps f and g (i.e., commuting squares) from i to p that are right homotopic in the injective or projective model structure.
	jdc.math.uwo.ca /papers/obstruction.txt (7257 words)

	10doster.htm Conjugacy in Dynamical Systems
		The bifurcation diagrams, in particular, seem to exhibit the same period doubling and chaotic behavior of the two families, although in different directions.
		If you begin with x [0, 1] in the upper left of the diagram and follow either route to the lower right, you must get the same result: H converts x in [0, 1] into u in [-2, 2].
		This conjugacy explains why the bifurcation diagrams (when x is a real variable) and the parameter plane diagrams, i.
	www.woodrow.org /teachers/mi/1993/10doster.html (2820 words)

	Springer Online Reference Works (Site not responding. Last check: )
		This, in particular, gave a solution to Thom's problem of constructing commutative cochains over the rationals.
		-functor together with its adjoint, the realization functor of a commutative differential graded algebra, induce an equivalence of homotopy categories between the homotopy category of simply-connected rational spaces with finite Betti numbers and the homotopy category of rational commutative differential graded algebras,
		Rational homotopy invariants of a space are most easily obtained by means of constructions in the category of commutative differential graded algebras.
	eom.springer.de /s/s120310.htm (412 words)

	commutative diagram@Everything2.com
		To say that a diagram is commutative means the following.
		-> B be two ways of chasing arrows, or paths, around the diagram (only going forward on the arrows).
		For example, let f be a map from A to B, g be a map from B to C, and h be a map from A to C. If the diagram
	everything2.com /index.pl?node_id=1183641 (149 words)

	Universal Framework for Science and Engineering - Part 5: Category theory - The Code Project - C# Libraries
		Another feature of the Category theory is commutative diagrams.
		However, the calculation of Herzsprung-Rassel Diagram (Part 2) of 100,000,000 or more stars takes a few of seconds.
		I had had an attempt at calculating the tensor product of two commutative algebras with four generators and two relations.
	www.codeproject.com /cs/library/UniversalEnggFrmwork5.asp (911 words)

	Limit and Colimit
		Let d be a commutative diagram on a given graph g.
		In other words, there is one morphism from u to v that makes the diagram commute.
		The morphism fg maps u into u, and since the diagram commutes, this has to be the identity morphism from u into u.
	www.mathreference.com /cat,limit.html (531 words)

	PlanetMath: categorical pullback
		, or a pullback square, is a commutative diagram
		, usually called a pushout square, is a commutative diagram
		Cross-references: isomorphism, cone over, terminal, object, commutative diagram, morphisms
	www.planetmath.org /encyclopedia/Pullback3.html (116 words)

	Venn Diagram Self-Test with active javascripted images
		On a separate piece of paper, re-create the blank Venn diagram shown in the problem.
		Then shade in the parts of this diagram which correspond to the named set.
		Finally, check your answer by moving your mouse pointer over the blank Venn diagram: the answer will appear.
	math.uww.edu /faculty/mcfarlat/143venn.htm (182 words)

	McLarty: Elementary Categories, Elementary Toposes (Site not responding. Last check: )
		The definition of (binary) product diagrams can be generalized to a product diagram for any finite number of objects.
		Every object (with identity) is a product diagram for itself (so that we have such products of a single object in every category).
		Given a category A, we can form the arrow category A^2 (this may also be interpreted as the category of all functors from the category 2 to A with natural transformations as arrows).
	gtps.math.cmu.edu /cebrown/notes/mclarty.html (7588 words)

	IntegraWorks - a program idea (Site not responding. Last check: )
		You can include spreadsheet results, commutative diagrams (math), pictures, movies, etc., etc. The possibilites are just about endless, because each feature will be implemented in a separate plug-in.
		For example, a math equation can be inside a commutative diagram, which in turn is embedded in your document's text.
		This would produce a little diagram showing finger placement on a guitar, as well as showing open strings, stopped strings, and capo or Barre chord position.
	chris.heathens.co.nz /idea.html (1035 words)

	Math 720
		Use part a) to show that any exact sequence can be obtained by “splicing” together short exact sequences.
		(The snake lemma) Consider the commutative diagram of modules with exact rows:
		Show that if the columns are exact and the bottom two rows are exact, then so is the top.
	www.ndsu.nodak.edu /ndsu/coykenda/M721.2.S2001.htm (96 words)

	Commutative diagram (Site not responding. Last check: )
		In mathematics, especially the many applications of category theory, a commutative diagram is a diagram ofobjects and morphisms such that, when picking two objects, one can follow any paththrough the diagram and obtain the same result by composition.
		Similarly, the square above is commutative if y
		Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative ifevery polygonal subdiagram is commutative.
	www.therfcc.org /commutative-diagram-178055.html (112 words)

	1.4 Hutchings' theory of integration
		form a ladder similar to the one in (2), and, in fact, they combine with the ladder in (2) to a single commutative diagram:
		Just like singular knots had symbols which were simplar combinatorial objects (chord diagrams), so do toplogical relators have combinatorial symbols:
		is canonically isomorphic to the space spanned by all ``relator symbols'', chord diagrams with n-2 chords and one
	www.math.toronto.edu /~drorbn/papers/Species/1_4Hutchings_theory_integra.html (909 words)

	[No title]
		Steven Smith wrote the documentation for the commutative diagram macros.
		* Diagram, macros for LaTeX: Construction of commutative diagrams.
		* universal mapping property: Construction of commutative diagrams.
	www.wisdom.weizmann.ac.il /~/TeX/info/eplain-4 (440 words)

	Q550 Models in Cognitive Science, Prof. Kruschke
		Make commutative diagrams of DFM and FLMP applied to letter perception.
		For an example of this sort of commutative diagram, see the end of the reading on the web regarding Newton's model of gravity, and see the
		326, should all be inside the "formal transformation" portion of your diagram.
	www.indiana.edu /~jkkteach/Q550/Spring2001/exercise_wk02.html (186 words)

	Derived Functors (Site not responding. Last check: )
		Consider the following diagram where first row is exact and second is a complex.
		, such that last square of above diagram becomes commutative, the required map must be the following factorization (proving uniqueness):
		and because last row of above commuting diagram is complex.
	www.imsc.res.in /~sgautam/main/node7.html (409 words)

	The TeX Catalogue OnLine, Entry for diagrams, Ctan Edition (Site not responding. Last check: )
		– Paul Taylor's long-established commutative diagram macros, which are designed to provide high power in a standard (La)TeX environment; and
		– Kris Rose and Ross Moore's xypic package which can be used for a variety of graphs and diagrams.
		The archive does not offer direct facilities to download this collection of ‘competing’ packages as a single whole.
	www.tex.ac.uk /tex-archive/help/Catalogue/entries/diagrams.html (136 words)

	A techexplorer-Enhanced Document
		If you would like to see what the above display looks like when techexplorer handles the whole screen, click here.
		The following example is a commutative diagram from an algebraic geometry paper.
		We've use macros within the TeX source document to represent the repeated elements in the diagram.
	www.math.fsu.edu /~seppala/JulyWorkshop/embed.html (376 words)

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