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Topic: Category of small categories

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category theory

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kernel category theory

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	Category theory - Wikipedia, the free encyclopedia
		Categories appear in most branches of mathematics, in some areas of theoretical computer science and mathematical physics, and have been a unifying notion.
		Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1945, in connection with algebraic topology.
		Such a process is called a functor, and it associates to every object of one category an object of another category, and to every morphism in the first category a morphism in the second.
	en.wikipedia.org /wiki/Category_theory (2372 words)

	Bicategory - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, a bicategory is a concept in category theory used to extend the notion of sameness (i.e.
		In a bicategory these 1-cells form a small category themselves by introducing mappings s, t, u,...
		The category of small categories, Cat, forms a bicategory with small categories as 0-cells, functors as 1-cells, and natural transformations as 2-cells.
	en.wikipedia.org /wiki/Bicategory (247 words)

	Beard and Moustache Categories
		Bushy; small, upward pointing ends; areas past the corner of the mouth must be shaved.
		Small pointed goatee, clearly separated from the moustache, which is especially prominent.
		Competitors will enter in the category of their choosing but may be placed into a different category if they do not meet the specifications for the chosen category.
	www.worldbeardchampionships.com /Categories/categories.htm (291 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		A related problem is that, if C is a small category, then NC is fibrant iff C is a groupoid.
		Besides an aesthetic objection to Thomason's model category structure, I have a practical one: Thomason uses the second subdivision followed by categorical realization as the functor going from simplicial sets to small categories inducing the equivalence of homotopy categories.
		There has also been quite a lot of work on model category structures for n-categories and related gadgets; however, when restricted to ordinary categories this work generally gives the homotopy equivalence between the category of simplicial 1-types and the category of small groupoids.
	www.lehigh.edu /~dmd1/sc55 (664 words)

	Emmanuel Haucourt: Abstract (Site not responding. Last check: 2007-11-06)
		A loop-free category is an epi-reflective subcategory of the category of small categories.
		The interest in these categories relies on the fact that the fundamental category of a po-space is always a loop-free category.
		For example, there is a van Kampen theorem for the functor Pi_1 whose codomain is the category of loop-free categories.
	www.math.aau.dk /~raussen/GETCO/A03/haucourt.html (152 words)

	Manuscript Categories
		In addition, the manuscripts in Category I (with the exception of the fragmentary early papyri, which are too short to classify this way, and 1175, which is block-mixed with the Byzantine text in Paul and the Catholic Epistles) are all very pure representatives of their types.
		Although it is not explicitly stated, the manuscript is probably Category II in John and Category III in Matthew.
		Listed as "Category III with reservations, but higher in the Catholic Epistles." In fact a sister or nearly of 1505, and should be classified accordingly.
	www.skypoint.com /~waltzmn/MSCategories.html (1592 words)

	Rings, modules, and algebras in infinite loop space theory, by Anthony D. Elmendorf and Michael A. Mandell (Site not responding. Last check: 2007-11-06)
		We give a new construction of the algebraic K-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output.
		The framework we use is the concept of multicategory, a generalization of symmetric monoidal category that precisely captures the multiplicative structure we have present at all stages of the construction.
		Our method ends up in Smith's category of symmetric spectra, with an intermediate stop at a new category that may be of interest in its own right, whose objects we call symmetric functors.
	www.math.uiuc.edu /K-theory/0680 (148 words)

	Mitchell's problem (Site not responding. Last check: 2007-11-06)
		There is a sketch, S1, for categories with finite products, in the sense that the category of models of this sketch is the category of small categories with chosen finite products..
		h(C) is given by a kind of syntactic "term" construction, so it is not any nice recognizable category* when C is a known category.
		If C were already imbedded in a "too large" category C' with pullbacks, such as the presheaf category, then a good thing to look at would be the image of h*(C) in C'.
	www.seas.upenn.edu /~sweirich/types/archive/1988/msg00118.html (356 words)

	Double Categories, 2-Categories, Thin Structures And Connections (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		The main result is that two possible structures which may be imposed on an edge symmetric double category, namely a connection pair and a thin structure, are equivalent.
		A full proof is also given of the theorem of Spencer, that the category of small 2-categories is equivalent to the category of edge symmetric double categories with thin structure.
		2 Pullback and pushout squares in a double category with conne..
	citeseer.ist.psu.edu /brown99double.html (397 words)

	Unicode Character Database
		The files with a small number of properties are listed first, followed by the files with a large number of properties: DerivedCoreProperties.txt, DerivedNormalizationProps.txt, Proplist.txt, and UnicodeData.txt.
		Most of these have the Pd General Category, but some have the Sm General Category because of their use in mathematics.
		Bidi_Class (L, AL, R) (4) These are the categories required by the Bidirectional Behavior Algorithm in the Unicode Standard.
	www.unicode.org /Public/UNIDATA/UCD.html (6772 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Subject: categories: Kleisli bi-categories Dear Category Theorists, I'm looking for a reference on the following bi-categorical variant of the construction of Kleisli categories.
		For example, $\cat C$ is the category of small categories and $\cat D$ is the category of small categories with finite colimits.
		Constructing (in the usual way) the Kleisli category $\cat K$ for $F$ leads to a bi-category since the universal property used to define the composition in $\cat K$ holds only up to a unique natural isomorphism.
	www.mta.ca /~cat-dist/catlist/1999/kleisli-bi (223 words)

	small pine sofa table
		Small End Table - Wood End Table, Wood Crafts, woodcrafts, pine wood, country...
		...is supported with a base with two small drawers.
		small pine sofa table and antique pine dresser miami websites.
	all-homequarters.com /6/42/small-pine-sofa-table.html (142 words)

	Lecture Notes
		small categories contain more defining features; therefore, FC model would predict that there should be more Stage 2 processing for small categories and thus longer RTs
		Prototypes are often supplied as “better” examples of a category (Mervis, Catlin, and Rosch, 1976).
		Prototypes receive more priming from category names and are judged more quickly (Rosch, 1975b) “fire engine red” vs. “muddy red”
	www.alleydog.com /cognotes/semanticmem.html (274 words)

	Category Theory for Computer Science
		Cartesian closed categories and the simplytyped lambda calculus.
		the category of automata (nondeterministic finite automata with one initial state and a set of accepting states) and automata morphisms (Aut)
		Using Category Theory to Design Implicit Conversions and Generic Operators.
	www.daimi.au.dk /~nygaard/CTfCS (620 words)

	Categories (Site not responding. Last check: 2007-11-06)
		Hurricane Andrew came ashore in Florida August 1992 as a Category 4 hurricane.
		Pressure 28.50 to 28.93 inches accompanied by a storm surge of 6 to 8 feet.
		Pressure 27.17 to 27.90 inches accompanied by a storm surge of 13 to 18 feet..
	weather.networkidl.net /categories.html (195 words)

	Seminários de TEORIA DAS CATEGORIAS
		With each variety V of algebras we associate a theory Th(V), which is the dual of the subcategory of all retracts of V-free algebras on finitely many generators.
		This gives a duality between the category of all varieties and that of all Cauchy-complete small categories with finite products.
		We further describe a duality betweeen the category of all quasivarieties and the category of small lex categories with enough regular projectives.
	www.mat.uc.pt /~categ/seminars/1997/17Fev97.html (88 words)

	HofPrints: Simplicial and categorical comma categories (Site not responding. Last check: 2007-11-06)
		Costenoble, Steven R. (2000) Simplicial and categorical comma categories.
		We show here that the correct weak equivalences are the ``weak fibre homotopy equivalences'' defined by Latch.
		We also construct a model category structure on the category of simplicial sets over NO in which the weak equivalences are the weak fibre homotopy equivalences.
	hofprints.hofstra.edu /documents/disk0/00/00/00/02/index.html (52 words)

	Decompositions of categories over posets (Site not responding. Last check: 2007-11-06)
		from the barycentric subdivision sdV of V to the category of small categories, such that, for every increasing sequence
		) is the category whose objects are the sequences
		Quillen's category or the category of orbits with isotropy groups in W.
	www.maths.abdn.ac.uk /~stc2001/abstracts/Slominska/Slominska.html (141 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Subject: categories: Cat as a model category Here's a question I've already asked on the algebraic topology mailing list.
		I received several very interesting replies, but there seems to be little published and I'm curious what else is out there: I have Thomason's 1980 paper "Cat as a closed model category." Are there any other references for model category structures on Cat, the category of small categories?
		Subject: categories: Re: Cat as a model category Date: Wed, 03 Nov 1999 16:43:12 EST The McGill Ph.D. thesis of my student, Murray Heggie, deals with closed model structures in Cat and in presheaf toposes.
	www.mta.ca /~cat-dist/catlist/1999/cat-as-model-cat (173 words)

	Topos theory (from mathematics, foundations of) -- Encyclopædia Britannica
		The quest for rigour > Category theory > Topos theory
		The original purpose of category theory had been to make precise certain technical notions of algebra and topology and to present crucial results of divergent mathematical fields in an elegant and uniform way, but it soon became clear that categories had an important role to play in the foundations of mathematics.
		It embraces the subjects of arithmetic, geometry, algebra, calculus, probability, statistics, and many other special areas of research.
	www.britannica.com /eb/article?tocId=35466 (757 words)

	Atlas: On flexibility for $2$-monads by G. M. (Max) Kelly (Site not responding. Last check: 2007-11-06)
		We go on to observe that, when T is flexible, T-algebra structure can be transported along an equivalence; and we end with an application of this to coherence results.
		(A small part of these results was presented at the 1995 Cambridge meeting, but was never published.)
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-41.
	atlas-conferences.com /c/a/j/f/41.htm (161 words)

	Theory and Applications of Categories
		Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads
		On the monadicity of categories with chosen colimits
		A note on the exact completion of a regular category, and its infinitary generalizations
	www.tac.mta.ca /tac (961 words)

	PHP Help: PHP Help Forums -> category management
		Return the currently pointed key..value pair in the passed array, and advance the pointer to the next element', CAPTION, 'each');" onmouseout="return nd();">each category name and where it was located in the hierarchy, like: /outdoor/nighttime/campfires.
		Each category would require at least one subcat (perhaps could just have the same desc as the category for small categories with no logical subcats)
		This makes it simple for the user to select a category and then have just the subcats for that category displayed to narrow down the search
	www.phpfreaks.com /forums/index.php?showtopic=48658 (548 words)

	Lonewacko: Immigration Archives
		It was posted from a small college in California's Central Valley.
		In the "small world, eh" dep't, there's also a link between the AILA and Rep. Chris Cannon.
		Those who support his or the similar plans are actually a small but powerful minority consisting of not just businesses but the racial lobby, the media, and the far left.
	lonewacko.com /blog/archives/cat_immigration.html (15909 words)

	Zyra's CATEGORIES - Zyra's website content listed by category
		But, better start somewhere, so here's a few categories to be going on with...
		The BEAUTY category, including hair and skincare, cosmetics, a variety of references towards the aim of looking good.
		Photographic category including photography related items; camera insurance, photography websites, discussion of merits of different image capture systems, and other photographic stuff.
	www.zyra.org.uk /category.htm (4193 words)

	Boat Plans OnLine - Categories
		Top Categories » Plans - Small Boats » All
		Most can be used with oars, sail or small outboards.
		Also see the dinghies category for small boats use sail, oars and outboards.
	www.boatplans-online.com /categories.php?id=1 (32 words)

	Shareware, Freeware, Trials. Offline Browsers & Explorer Replacements.. (Site not responding. Last check: 2007-11-06)
		SoftSamba is a software directory with software organised into small specific lists which can be sorted by price, date or name.
		In the index below the number after each category name is the number of programs in that category.
		It always includes programs in all subcategories of that category.
	www.softsamba.co.uk (159 words)

	Category Theory Definition List
		These definitions can all be found in Herrlich and Strecker's nice introduction to Category Theory.
		If you came here hoping to find some definitions instead of lists of terms, see my page of links to on-line category thory resources.
		Natural Functor from a Category to its Quotient Category
	www.maths.tcd.ie /~icecube/Cats/defs.html (48 words)

	ZYRA / Zyra's website www.zyra.org.uk
		Have a good look around and feel free to wander off into the conceptual hyperstructure if you like.
		The Guided Tour continues on this channel, by which you can follow me through into #THIS LINK, or, if you prefer a more indexed approach, you have a choice of looking for items by category, or alphabetically, or in order of what's new, or in random order!
		There is so much stuff on this site it has had to be organised in various ways to make it easier to look around!
	www.zyra.org.uk (560 words)

	Frequently Asked Questions
		Search by topic using the drop-down "Choose Category" menu
		Narrow down your search by using both the category menu and search term entry field
		Click on any question to view its full answer and related references
	www.irs.gov /faqs (218 words)

	GRAMMY.com
		For recordings released during the Eligibility Year October 1, 2002 through September 30, 2003
		Note: More or less than five nominations in a category is the result of a tie.
		Best Small Ensemble Performance (with or without Conductor)
	www.grammy.com /awards/grammy/46noms.aspx (3849 words)

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