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	Yoneda lemma - Wikipedia, the free encyclopedia
		The Yoneda lemma suggests that instead of studying the (small) category C, one should study the category of all functors of C into Set (the category of sets with functions as morphisms).
		The Yoneda lemma remains true for preadditive categories if we choose as our extension the category of additive contravariant functors from the original category into the category of abelian groups; these are functors which are compatible with the addition of morphisms and should be thought of as forming a module category over the original category.
		The Yoneda lemma then yields the natural procedure to enlarge a preadditive category so that the enlarged version remains preadditive — in fact, the enlarged version is an abelian category, a much more powerful condition.
	en.wikipedia.org /wiki/Yoneda_lemma (687 words)

	yoneda lemma
		The Yoneda lemma in category theory allows the embedding of any category in a category of functors defined on that category, and clarifies how the embedded category relates to the other objects in the larger functor category.
		Generally speaking, the Yoneda lemma suggests that instead of studying the (small) category C, one should study the category of all functors of C into Set (where Set is the category of all sets with functions as morphisms).
		In the case of a ring R, the extended category is the category of all right modules over R, and the statement of the Yoneda lemma reduces to the well-known isomorphism
	www.fact-library.com /yoneda_lemma.html (661 words)

	Citations: atory, Cambridge, June 1995. To appear in Theoretical Computer Science - Wagner, in, Report, Cambridge, ... (Site not responding. Last check: 2007-10-07)
		In [SMM95] the Yoneda lemma is used in the definition of a completion of monoidal closed categories.
		The use of the Yoneda lemma for the completion of generalized metric spaces is new, but it is suggested by an....
		In [Sas94] the Yoneda lemma is used in the definition of a completion of monoidal closed categories.
	citeseer.ist.psu.edu /context/317772/0 (816 words)

	[No title]
		Moreover, the representable functors HX are proje* ctive objects in mod C by Yoneda's* lemma, and they are also injective since C is tria* *ngulated.
		X is an isomorphism by Lemma 2.1, and therefore FX (A) is of finite length over X for all A. We conclude that X is endofinite, and this * *finishes_ the proof.
		Q(HX) with the indecomposable injective objects in Mod* * C0=T by Lemma 2.1.
	hopf.math.purdue.edu /KrauseH-Reichenbach/endofiniteness.txt (6691 words)

	[No title]
		The category TI is a Serre subcategory of Mod C0 by Lemma 3.2 since I is cohomological, and therefor* *e HZ belongs to TI.
		Mod (C=B)0 is just the restricted Yoneda functor hC=B. We proceed with the proof of Theorem C which we recall for the convenience of* * the reader.
		We ha* ve I = I(CI)by the preceding lemma, and a combination of Lemma* 3.10 and Theorem 4.2 then shows that CI is a smashing subcategory of C. Given a smashing subcategory* * B, we have C(IB)= B by Theorem 4.2.
	hopf.math.purdue.edu /KrauseH/smash.txt (13290 words)

	From the Yoneda lemma to categorical physics
		One way to think of the Yoneda lemma is precisely this: that the objects of any category can be interpreted as sets with extra structure.
		The Yoneda lemma says that this "set with extra structure" knows everything you'd ever want to know about the object c.
		In fact there is another version of the Yoneda lemma that uses the morphisms to c instead.
	www.lns.cornell.edu /spr/1999-09/msg0017972.html (1025 words)

	Yoneda's Lemma
		Thus y is a co-functor from &on; to Transform(&on;, Set) and its transpose, Yoneda = transpose(y), is a functor from &on; to coTransform(&on;, Set).
		Yoneda Functor is also known as the Yoneda Embedding: it embeds C fully and faithfully in coTransform(C,Set).
		Thus Yoneda's lemma gives us a transformation, B, conjoinable between K and evaluation in coTransform(C,Set)×dual-C: and B's images of identities are all isomorphisms in Set, which makes B an isomorphism in naTrans(K, evaluate), within Transform(coTransform(C,Set)×dual-C, Set).
	www.chaos.org.uk /~eddy/math/arrow/Yoneda.html (1820 words)

	YONEDA (Site not responding. Last check: 2007-10-07)
		Search the YONEDA Family Message Boards at Ancestry.com (if available).
		Search the YONEDA Family Resource Center at RootsWeb.com (if available).
		Find graves of people named YONEDA at Find-a-Grave.com (or add one that you know).
	www.worldhistory.com /surname/US/Y/YONEDA.htm (73 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		The simplification comes from a systematic use of constructive category theory (formalized in type theory in the style of Huet and Saibi, and previously Peter Aczel and Michael Hedberg), where each hom-set in a category is equipped with an explicit relation of equality of arrows ("hom-setoid").
		More specifically, we use the Yoneda lemma for cartesian closed categories, that is, the fact that the Yoneda functor is full and faithful and preserves the cartesian closed structure.
		The Yoneda lemma only refers to basic notions (such as category, functor, natural transformation, and functor category) and is just about the first non-trivial proposition in category theory.
	www.cs.chalmers.se /Cs/Newsletter/Veckoblad/tmp/letter.960208-13:08:29-715 (460 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		The contents of this talk was later named by Mac Lane as Yoneda lemma.
		So, the famous Yoneda lemma was born in Gare du Nord.
		Until 1976, Yoneda was a professor of the department of mathematics at Gakushu-in University in Tokyo, and he took a professorship in 1977 at the newly established department of information science at the University of Tokyo, where he had 15 MSc.
	www.mta.ca /~cat-dist/catlist/1999/yoneda (593 words)

	J.J.M.M. Rutten (Site not responding. Last check: 2007-10-07)
		Next a topology for generalized ultrametric spaces is defined, which combines both the Scott topology on preorders and the ordinary \epsilon -ball topology on ultrametric spaces, in a way that preserves the nice properties of both.
		It is shown that the closure operator corresponding to this generalized Scott topology, as we have called it, arises naturally via, again, the Yoneda Lemma.
		This lemma is finally applied once more in the construction of a generalized lower powerdomain.
	www.utm.edu /staff/jschomme/topology/c/a/a/f/73.htm (226 words)

	Lambek and Scott: Introduction to higher order categorical logic (Site not responding. Last check: 2007-10-07)
		The Yoneda Lemma states that if A is locally small and F:A^op -> Sets is a functor, then Nat(yA,F) is isomorphic to the set FA (in fact, naturally in A and F).
		The Yoneda Lemma is used to prove that the Yoneda functor is full and faithful.
		Prove that the Yoneda functor is an embedding.
	www.andrew.cmu.edu /user/cebrown/notes/lambekscott.html (4587 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		The second, symmetries, and also fractals were used in musical composition, they appear also in nature and play a crucial role in mathematics as well as in physics.
		The third, the Yoneda philosophy, says that in order to understand an object, just walk around it.
		In mathematics, the Yoneda Lemma has important implications in homological algebra, algebraic topology and algebraic geometry just to name a few.
	www.epos.uni-osnabrueck.de /books/m/ma_nl004/pages/37.htm (474 words)

	Archive of Formal Proofs (Site not responding. Last check: 2007-10-07)
		This development proves Yoneda's lemma and aims to be readable by humans.
		It only defines what is needed for the lemma: categories, functors and natural transformations.
		An updated version of this entry is available in the development version of AFP.
	afp.sourceforge.net /entries/Category.shtml (49 words)

	categories: Enriched category theory, again (Site not responding. Last check: 2007-10-07)
		The first is a generalization of the enriched Yoneda lemma.
		I don't remember if any completeness or cocompleteness assumptions on D are necessary here because I always assume D is bicomplete.
		I think the proof is the same as the usual Yoneda lemma.
	north.ecc.edu /alsani/ct02(1-2)/msg00021.html (394 words)

	yoneda (Site not responding. Last check: 2007-10-07)
		In fact, this is a special case of Yoneda's bijection.
		k : (inverse j) := (yoneda_bij_inv (yoneda y) x).
		That is one would expects to do the proof of the following lemma by
	www.math.unifi.it /~maggesi/coq/zariski/html/yoneda.html (251 words)

	Re: Does a fundamental time exist in GR and QM?
		(Ultimately, category theory rejects that distinction as meaningless.) In fact, james said the Yoneda lemma ensures that every category may be so interpreted, modulo set/class distinctions.
		Since I never got the hang of Yoneda, I'll believe him.
		Therefore, the answer to your question is really "No.", but it may not be obvious right away how to interpret a category as Set with extra structure, so I'd still think in terms of categories.
	www.lns.cornell.edu /spr/1999-09/msg0017971.html (318 words)

	[No title]
		The proof of Theorem A is based on a reformulation of condition (G2) which is* * given in Lemma 3.
		(S; X) is surjective`for all S 2 S. This follows from* * Yoneda's lemma if we take X0 = S2S0XS where XS = (S;X)S. (1) To prove that bSis abelian it is sufficient to show that every map in S h* *as a weak kernel.
		bT-f!bS: The Yoneda* functor is cohomological and f* is exact.
	hopf.math.purdue.edu /KrauseH/brown-II.txt (2633 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		Mazzola and Hofmann (1989); Mazzola (1990a), and we will stress one main argument again here: Classification is nothing else than the task of totally understanding an object.
		This is Yoneda’s lemma in its full philosophical implication, in fact, the isomorphism class of an object
		is equivalent to that of its contravariant Yoneda functor
	www.epos.uni-osnabrueck.de /books/m/ma_nl004/pages/61.htm (431 words)

	Abstract of: Generalized ultrametric spaces: completion, topology, and powerdomains via the Yoneda embedding (Site not responding. Last check: 2007-10-07)
		Abstract of: Generalized ultrametric spaces: completion, topology, and powerdomains via the Yoneda embedding
		Title of the page: Abstract of: Generalized ultrametric spaces: completion, topology, and powerdomains via the Yoneda embedding
		Interestingly, all constructions are formulated in terms of (an ultrametric version of) the Yoneda (1954) lemma.
	db.cwi.nl /rapporten/abstract.php?abstractnr=533 (143 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		CS-R9636 Generalized Metric Spaces: Completion, Topology, and Powerdomains via the Yoneda Embedding M.M. Bonsangue Vrije Universiteit Amsterdam De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands email: marcello@cs.vu.nl F.
		AMS Subject Classification (1991): 68Q10, 68Q55 CR Subject Classification (1991): D.3.1, F.1.2, F.3.2 Keywords and Phrases: preorder, quasimetric, generalized metric, metric, enriched category, Yoneda lemma, completion, topology, powerdomain.
		Generalized {\em ultra}metric spaces: completion, topologies, and powerdomains via the Yoneda embedding.
	homepages.cwi.nl /~janr/papers/abstracts/abstract.CS-R9636 (202 words)

	Abstract of: Generalized metric spaces: completion, topology, and powerdomains via the Yoneda embedding (Site not responding. Last check: 2007-10-07)
		Abstract of: Generalized metric spaces: completion, topology, and powerdomains via the Yoneda embedding
		Title of the page: Abstract of: Generalized metric spaces: completion, topology, and powerdomains via the Yoneda embedding
		All constructions are formulated in terms of (a metric version of) the Yoneda (1954) embedding.
	db.cwi.nl /rapporten/abstract.php?abstractnr=588 (142 words)

	Category theory - FreeEncyclopedia (Site not responding. Last check: 2007-10-07)
		This motivating example of sheaves is generalized by considering pre-sheaves on arbitrary categories: a pre-sheaf on C is a functor defined on C
		The Yoneda lemma explains that often a category C can be extended by considering a category of pre-sheaves on C.
		Set are completely known and easy to describe; this is the content of the Yoneda lemma.
	openproxy.ath.cx /ca/Category_theory.html (2075 words)

	Practical Foundations of Mathematics
		Describe the category (analogous to that in Lemma 4.5.16) of which the function-space Y
		A canonical choice amongst equivalent paths is given by reducing these redexes from left to right; this is called a standard reduction: see [Bar81, Definition 11.4.1].
		x F,G) by the Yoneda Lemma, Theorem 4.8.12(c).] Deduce that the Yoneda embedding preserves function-spaces.
	www.cs.man.ac.uk /~pt/Practical_Foundations/html/s4e.html (1261 words)

	What is Yoneda lemma? : Abaara fun facts and uncommon knowledge (Site not responding. Last check: 2007-10-07)
		The Yoneda lemma suggests that instead of studying the (small) category C, one should study the category of all functors of C into Set (the category of sets with functions as
		is called the Yoneda embedding and it is "natural" in the sense that every functor C → D induces a commutative diagram
		The Yoneda lemma remains true for preadditive categories if we choose as our extension the category of
	www.abaara.com /pac/Yoneda_lemma (666 words)

	Logic and Semantics Seminar - 10th October, 1997: Luca Cattani
		The objects of the base category are to be thought of as consisting of path objects, or computation-path shapes.
		The Yoneda Lemma then justifies an intuition that a presheaf can be thought of as specifying for a typical path object the set of computation paths of shape that object.
		An open map between two presheaves is then defined to be a natural transformation satisfying a particular path lifting property.
	www.cl.cam.ac.uk /Research/LS/Talks/1997_98/97_10_10.Abstract.html (413 words)

	Casual Category Theory - Spring 2000
		If time permits we will state the weak version of Yoneda Lemma for V-categories.
		This is supposed to cover Yoneda, limits (ends) and adjunctions.
		The talk will consist in a condensed presentation of the material taught by Glynn last semester.
	www.brics.dk /~varacca/CCT/cct-spring00.html (504 words)

	Citations: Fibrations and Yoneda's lemma in a 2-category - Street (ResearchIndex)
		Street, Fibrations and Yoneda's Lemma in a 2-category, in: Sydney Category Seminar, LNM
		Street, Fibrations and Yoneda's Lemma in a 2-category, in: Sydney Category Seminar, LNM 420, Springer-Verlag 1974, 104-133
		....brations for them so that the Yoneda object on M does correspond to the object of discrete brations on it.
	citeseer.ist.psu.edu /context/374925/0 (2231 words)

	Transactions of the American Mathematical Society
		It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others.
		The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy coherent form of the Yoneda lemma and of Kan extensions.
		This latter area is linked with the theory of generalised derived functors.
	www.ams.org /tran/1997-349-01/S0002-9947-97-01752-2/home.html (902 words)

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