
	Where results make sense

Topic: Coproduct

Related Topics

Limit (category theory)

Direct limit

Pullback (category theory)

Behelit

Line feed

148 BCE

Thermostat

Chromatin

Healthcare

Hryvnia

F M Khan

In the News (Fri 27 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Coproduct - Wikipedia, the free encyclopedia
		The coproduct indexed by the empty set (that is, an empty coproduct) is the same as an initial object in C.
		In the case of topological spaces coproducts are disjoint unions on the underlying sets, and the open sets are sets open in each of the spaces, in a rather evident sense (see disjoint union (topology)).
		In the category of pointed spaces, fundamental in homotopy theory, the coproduct is the wedge sum (which amounts to joining a collection of spaces with base points at a common base point).
	en.wikipedia.org /wiki/Coproduct (454 words)

	Disjoint union (topology) - Wikipedia, the free encyclopedia
		In topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology.
		The name coproduct originates from the fact that the disjoint union is the categorical dual of the product space construction.
		This shows that the disjoint union is the coproduct in the category of topological spaces.
	en.wikipedia.org /wiki/Direct_sum_%28topology%29 (351 words)

	Coproduct -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		Coproducts are actually special cases of (Click link for more info and facts about colimit) colimits in category theory.
		It follows that if coproducts exists in a given category (they need not) they are unique (Click link for more info and facts about up to) up to a unique ((biology) similarity or identity of form or shape or structure) isomorphism that respect the injections.
		The coproduct indexed by the (Click link for more info and facts about empty set) empty set (that is, an empty coproduct) is the same as an (Click link for more info and facts about initial object) initial object in C.
	www.absoluteastronomy.com /encyclopedia/c/co/coproduct.htm (531 words)

	Coproduct (Site not responding. Last check: 2007-10-07)
		On the other in the category of abelian groups (and equally for vector spaces) the coproduct called the direct sum consists of the elements of the product which have only finitely many nonzero (this therefore coincides exactly with the direct in the case of finitely many factors—so for "dramatically different").
		In the case of topological spaces coproducts are disjoint unions on the sets and the open sets are sets open in each of the spaces in a rather evident sense.
		In category of pointed spaces fundamental in homotopy theory the coproduct is the wedge sum amounts to joining a collection of spaces base points at a common base point).
	www.freeglossary.com /Coproduct (407 words)

	PlanetMath: disjoint union (Site not responding. Last check: 2007-10-07)
		This is the coproduct in the category of topological spaces.
		Of course, there are many categories where this usage is unnatural: In the category of pointed sets, the coproduct will be the disjoint union with the distinguished points identified.
		In the category of abelian groups, the coproduct is actually the sum.
	www.planetmath.org /encyclopedia/DisjointUnion.html (214 words)

	Encyclopedia: Coproduct
		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.
		In the mathematical field of topology a direct sum, direct disjoint sum or coproduct is an important universal construction for topological spaces.
		In mathematics, a pointed space is a topological space X with a distinguised basepoint x0 in X. Maps of pointed spaces are continuous maps preserving basepoints, i.
	www.nationmaster.com /encyclopedia/Coproduct (1261 words)

	Coproduct - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-07)
		In the case of topological spaces coproducts are disjoint unions on the underlying sets, and the open sets are sets open in each of the spaces, in a rather evident sense.
		The effects of corn milling coproducts on growth performance and diet digestibility by beef cattle : An article from: Journal of Animal Science
		Coproducts of coke in the United States, 1919-1947 (U.S. Dept. of the Interior, Bureau of Mines, information circular, I.C. 7504, June 1949)
	encyclopedia.worldsearch.com /coproduct_(category_theory).htm (543 words)

	Coproducts and Near Coproducts of Fuel Ethanol Fermentation from Grain (Site not responding. Last check: 2007-10-07)
		The type of coproducts that are produced depends on a number of factors, including conversion technology, feedstock and milling process (Turhollow and Heady, 1986).
		While it is difficult to foresee which coproducts will become the most successful, profits associated with the sale of a number of materials may become as important to the industry as innovations which increase the efficiency of the ethanol production process (Rendleman and Hohmann, 1993).
		Although it has been suggested that coproduct revenue can account for up to 40% of the income of an ethanol plant (Chang et al., 1995), it is difficult to put a value on novel coproducts because many that have been proposed do not yet have established markets (Spelman, 1994).
	res2.agr.gc.ca /publications/cfar/chap1_e.htm (16608 words)

	Recovery of solids and nutrients contained in corn wet milling coproduct streams using microfiltration membranes (Site not responding. Last check: 2007-10-07)
		Coproducts, such as corn gluten feed and corn gluten meal, are produced in parallel with starch in the corn wet milling process.
		These coproducts are high in fiber, protein, and soluble carbohydrates and must be concentrated, dewatered, and dried in an economical fashion.
		In this study, the suitability of stainless steel microfiltration (MF) membranes to dewater corn wet milling coproduct streams was investigated.
	www.aaccnet.org /meetings/99mtg/abstracts/acabb82.htm (286 words)

	[No title]
		By proposition 2.3, the coproduct (and Hopf algebra structure) on the E2-term E2*(R) = HH(H(R; Fp)) that is derived from the R-Hopf algebra structure on 16 VIGLEIK ANGELTVEIT AND JOHN ROGNES T HH(R) agrees with the algebraically defined structure on the Hochschild homol- ogy HH() of the commutative algebra = H*(R; Fp).
		The A-comodule structure is given on H(ko; F2) by restricting the coproduct on A, and on the algebra gene *ra- tors by (oe,~41) = 1 oe,~41and (oe,~22)= 1 oe,~22+ ~,21 oe,~41 (oe,~3)= 1 oe,~3+ ~,1 oe,~22+ ~,2 oe,~41.
		The A-comodule structure is given on H(tmf; F2) by restricting the coproduct on A*, and on the algebra generators by (oe,~81) = 1 oe,~81and (oe,~42)= 1 oe,~42+ ~,41 oe,~81 (oe,~23)= 1 oe,~23+ ~,21 oe,~42+ ~,22 oe,~81 (oe,~4)= 1 oe,~4+ ~,1 oe,~23+ ~,2 oe,~42+ ~,3 oe,~81.
	hopf.math.purdue.edu /Angeltveit-Rognes/vigleik.txt (12372 words)

	Creation Functions (Site not responding. Last check: 2007-10-07)
		Coproduct elements are usually created by the injections returned as the second return value from the cop<> constructor.
		Given a coproduct injection map m and an element of one of the constituents of the coproduct C, create the coproduct element version of e.
		Given a coproduct C and an element e of one of the constituents of C such that the type of that constituent is unique within that coproduct, create the coproduct element version of e.
	www.math.ufl.edu /help/magma/text168.html (207 words)

	Cobig, Coproduct, and Comma (410 lines)
		Date: Sun, 19 Mar 89 23:45:31 PST Cobig, Coproduct, and Comma Vaughan Pratt 3/19/89 It is eminently reasonable, whether you are a computer or a human, to schedule tasks on the basis of size.
		Coproducts in Set have no morphisms at all, being just sets.
		The coproduct C+D in Cat has morphisms, but only those of C and D separately.
	www.seas.upenn.edu /~sweirich/types/archive/1989/msg00037.html (2666 words)

	HUBBARD FEEDS INC : Beef - Corn Milling Coproducts for Beef Cattle (Site not responding. Last check: 2007-10-07)
		In the case of milling coproducts the alternatives are corn as an energy source and soybean meal for protein supplementation.
		When the price of coproduct feeds exceeds the price of corn on a dry matter basis but is lower than soybean meal, economics favor using the coproduct as a source of protein rather than energy.
		Coproducts will continue to be a major feed source for cattle operations as they keep pace with growth of the ethanol industry.
	www.hubbardfeeds.com /nmg/beef/beef_cornmilling.shtml (1408 words)

	Iowa Code 1999: Section 159A.3
		An office of renewable fuels and coproducts is created within the department and shall be staffed by a coordinator who shall be appointed by the secretary.
		The degree to which the renewable fuel or coproduct is currently developed for ready transfer to current engine technology.
		Conducting studies relating to the viability of producing or using renewable fuels and coproducts, and methods and schedules required to ensure a practicable transition to the use of renewable fuels and coproducts.
	www.legis.state.ia.us /IACODE/1999/159A/3.html (662 words)

	Product and Coproduct
		In the category of sets, the coproduct is the disjoint union.
		The coproduct of infinitely many rings or r modules is the direct sum.
		There is a coproduct however, namely the free group on two generators.
	www.mathreference.com /cat,prod.html (1156 words)

	Re: Question about Adjoints
		An important difference between zero, addition and subtraction and their categorical analogs is that these operations represent extra structure on a set, while having a zero object, coproducts of two objects, or cokernels of morphisms is merely a property of a category.
		A coproduct of the objects x and y is an object x+y equipped with morphisms i: x -> x+y and j: y -> x+y, that is universal with respect to this property.
		To understand this abstract nonsense, it's good to check that the coproduct of sets or topological spaces is just their disjoint union, while the coproduct of vector spaces or Hilbert spaces is their direct sum.
	www.lns.cornell.edu /spr/1999-07/msg0017047.html (2539 words)

	Pennsylvania Material Trader: Regulatory Information (Site not responding. Last check: 2007-10-07)
		A coproduct determination only applies to materials that will be applied to the land or used to produce products that are applied to the land, used for energy recovery, or used as a fuel.
		Although coproduct determinations do not need to be submitted for DEP approval, many facilities choose to submit documentation of the coproduct determination to their DEP regional office and request concurrence with the determination.
		If the proposed coproduct material is oil, a determination may only be made for oil refined from crude oil or synthetically produced oil, not contaminated by physical or chemical impurities, that will be used for energy recovery if the material has a minimum heat content (BTU value) comparable to the petroleum fuel it will replace.
	www.materialtrader.org /regulatory.asp (3347 words)

	PlanetMath: dual category (Site not responding. Last check: 2007-10-07)
		For example, a coproduct is a product on the opposite category; this can be seen by looking at the commutative diagram that completely specifies a coproduct, and noting that it is the same as the diagram specifying a product with the arrows reversed.
		More generally, an inverse limit is a direct limit on the opposite category; for this reason, it is sometimes called a colimit.
		In fact, this is often how contravariant functors are defined, and it is why most categorical theorems and constructions need not explicitly consider both cases.
	www.planetmath.org /encyclopedia/OppositeCategory.html (226 words)

	Corn Gluten Feed -- Composition, Storage, Handling, Feeding and Value
		Up to 93 percent of dent corn produced (including the corn equivalent of coproduct feeds from corn processing) is used as animal feeds.
		Corn gluten feed (CGF) is a coproduct of the wet milling industry.
		Coproducts such as wet corn gluten feed present challenges in handling, and mixtures that facilitate movement of the material may exceed the structural integrity of the storage unit.
	www.ext.nodak.edu /extpubs/ansci/dairy/as1127w.htm (2231 words)

	Practical Foundations of Mathematics
		In a poset, the initial object is the least element and the coproducts are joins (Definition 3.2.4); in particular they are falsity and disjunction for formulae under the provability order.
		Free (co)products and van Kampen's theorem Coproducts of algebras in general tend to be rather chaotic, Mon being typical.
		Coproducts of monoids are clearly relevant to formal languages, but one might think that the only other value of this construction is in universal algebra.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s54.html (1889 words)

	Estimating the Net Energy Balance of Corn Ethanol
		When energy use is allocated to the coproducts made during the ethanol conversion process, such as gluten meal, gluten feed, and corn oil, they conclude that the NEV of corn ethanol is 18,324 Btu/gal.
		For example, if energy used to produce ethanol is allocated between ethanol and coproducts based on their 10-year average market values, about 30 percent of energy used to produce ethanol should be assigned to the coproducts.
		When coproduct energy credits are added to the calculations, the NEV of corn ethanol is positive regardless of the type of milling used.
	www.ethanol-gec.org /corn_eth.htm (7290 words)

	Coproducts and Near Coproducts of Fuel Ethanol Fermentation from Grain
		While some of the coproduct research is centred at university and government laboratories, a great deal is being done collaboratively with industry.
		In addition to research being done specifically on grain-to-ethanol process byproducts, there is the whole area of value-added cereal components or near coproducts that is not necessarily connected to the ethanol industry but is still of significance as the industry may provide a low-cost source of raw material for extraction.
		They are trying to find solutions to the lack of value-added coproducts currently in the marketplace, and the associated high cost of recovery and separation of potential coproducts that have been identified.
	res2.agr.ca /publications/cfar/chap3_e.htm (4611 words)

	Practical Foundations of Mathematics
		The notion of stable (or universal) disjoint coproduct was recognised by the Grothendieck school (c.
		The bottom row is given to be a coproduct, whilst the squares are easily seen to be pullbacks, as they are defined in terms of products; then we conclude that the top row is also a coproduct.
		the components of the coproduct are disjoint, ie the square on the left is always a pullback.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s55.html (1478 words)

	Evaluation microfiltration membranes for the recovery of solids and nutrients in corn wet milling coproduct streams. (Site not responding. Last check: 2007-10-07)
		Evaluation microfiltration membranes for the recovery of solids and nutrients in corn wet milling coproduct streams.
		Coproducts must be dewatered and dried economically due to high levels of fiber, protein, and soluble carbohydrates.
		In this study, the feasibility of stainless steel MF membranes to concentrate corn wet milling coproduct streams was determined.
	www.aaccnet.org /meetings/2000/Abstracts/a00ma355.htm (355 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		Since objects are decomposable into a "quotient of a coproduct of generators" (Borceux, volume 1, page 151), this would give a decomposition into primes.
		A category E with finite coproducts is said to be extensive if for all objects x,y of E, the ``coproduct functor'' E/x x E/y --> E/(x+y) is an equivalence.
		The objects of Fam(C) are finite families (C_i)_{i\in I} and an arrow from (C_i)_I to (D_j)_J comprises a function f:I-->J and a family of arrows C_i-->D_fi in C. Fam(C) is the free category with finite coproducts on the category C. The connected (=prime) objects are precisely the singleton families.
	www.mta.ca /~cat-dist/catlist/1999/prime-objects (431 words)

	Reed Smith :: Library (Site not responding. Last check: 2007-10-07)
		The key definitions which determine whether a material is a "waste," is a "coproduct" or can be "dewasted" have been significantly altered and every prior determination of the regulatory status of a material must be carefully revisited.
		Anyone having a coproduct determination which does not fit the proposed delimiting criteria should be studying their situation very carefully.
		the ’coproduct’ definition, a person performing a coproduct determination shall evaluate chemical composition and threat of harm to the environment and public health in accordance with this section." The proposed coproduct shall not present a "greater threat of harm" than the use of an intentionally manufactured product or produced raw material.
	www.reedsmith.com /library/publicationPrint.cfm?itemid=3590) (1146 words)

Try your search on: Qwika (all wikis)