61. Computational Category Theory At Macquarie Computational category theory project group. People, projects, publications. http://www.ics.mq.edu.au/~mike/compcat/

Computational category theory projects at Macquarie Participants Michael Johnson Kit Dampney Kate Krastev Dominic Verity ... Robbie Gates Projects Case support for category theoretic specification of information systems Case support for modelling concurrency with n-categorical pasting schemes The theory of generalised distributivities Computational algebra and monoid theory (joint with Anne Heyworth, Leicester) Publications Until this page is better developed you can get some idea of some of the work we do by looking at the following publications, most (but not all) of which relate to computational category theory and what we seek to do with the tools these projects are developing. Recent Publications (updated September 2000) Selected Older Publications The International Computational Category Theory Project This site is part of The Computational Category Theory Project Groups Currently connected with this project are: Como, Italy Contact: R.F.C. Walters Walters@fis.unico.it University of North Wales, Bangor, Wales Contact: R. Brown

62. Oxford University Press: Logic Oxford University Press USA publishes scholarly works in all academic disciplines, bibles, music, children's books, business books, dictionaries, reference books, journals, text http://www.oup.com/us/catalog/general/subject/Mathematics/Logic/?view=usa&ci

63. Computational Category Theory At Mt Allison Computational Category Theory. Software, people. http://www.mta.ca/~rrosebru/compcat/compcat.html

The Computational Category Theory Project at Mount Allison University This site is part of The Computational Category Theory Project. Goals and Method. The aim of this project is the development of software on a wide variety of platforms for computing with mathematical categories and associated algebraic structures. Although writing on different platforms each group will undertake to make available programs for translating their input and output files to the formats of the other groups. Software developed at Mount Allison Graphical Database for Category Theory Java application - Version 1.0 (January 2000) mathcs.mta.ca/research/rosebrugh/gdct/ Developed in 1998, a Java applet: Category Theory Database Tools by J. Bradbury and R. Rosebrugh. Warning: The applet is a 700Kb download. Improved version coming 99/9. Completed in 1995, a menu-based C program: A Database of Categories Other Members Ronnie Brown School of Mathematics, University of Wales, Bangor, Wales Anne Heyworth MCS, University of Leicester, England ... Bob Rosebrugh

64. Category Theory Authors/titles Recent Submissions Title Model structures, categorial quotients and representations of super commutative Hopf algebras II, The case Gl(m,n) http://arxiv.org/list/math.CT/recent

arXiv.org math math.CT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Category Theory Authors and titles for recent submissions Fri, 29 Oct 2010 Wed, 27 Oct 2010 Tue, 26 Oct 2010 Fri, 22 Oct 2010 ... Tue, 19 Oct 2010 [ total of 10 entries: [ showing up to 25 entries per page: fewer more Fri, 29 Oct 2010 arXiv:1010.5934 pdf Title: Touchard like polynomials and generalized Stirling numbers Authors: G. Dattoli B. Germano M.R. Martinelli P.E. Ricci Subjects: Category Theory (math.CT) Wed, 27 Oct 2010 arXiv:1010.5304 pdf ps other Title: Note on star-autonomous comonads Authors: Craig Pastro Comments: 9 pages Subjects: Category Theory (math.CT) arXiv:1010.5397 (cross-list from math.AG) [ pdf ps other Title: Mirror stability conditions and SYZ conjecture for Fermat polynomials Authors: So Okada Subjects: Algebraic Geometry (math.AG) ; Category Theory (math.CT); Representation Theory (math.RT); Symplectic Geometry (math.SG) Tue, 26 Oct 2010 arXiv:1010.4956 pdf ps other Title: Dendroidal Segal spaces and infinity-operads Authors: Denis-Charles Cisinski Ieke Moerdijk Subjects: Category Theory (math.CT)

65. Theory And Applications Of Categories An electronic journal of category theory. Full text, free. http://www.tac.mta.ca/tac/

Editors Policy Subscriptions Authors - ... - Canada Theory and Applications of Categories ISSN 1201 - 561X Volume 24 - 2010 Bicategories of spans as cartesian bicategories Stephen Lack, R.F.C. Walters, and R.J. Wood, 1-24 abstract dvi ps pdf ... The Frobenius relations meet linear distributivity J.M. Egger, 25-38 abstract dvi ps pdf ... Joyal's arithmetic universe as list-arithmetic pretopos Maria Emilia Maietti, 39-83 abstract dvi ps pdf ... Monads as extension systems - no iteration is necessary F. Marmolejo and R. J. Wood, 84-113 abstract dvi ps pdf ... On a conjecture by J.H.Smith George Raptis, 114-116 abstract dvi ps pdf ... Topos theoretic aspects of semigroup actions Jonathon Funk and Pieter Hofstra, 117-147 abstract dvi ps pdf ... Transversal homotopy theory Jonathan Woolf, 148-178 abstract pdf On modified Reedy and modified projective model structures Mark W. Johnson, 179-208 abstract dvi ps pdf ... pdf F. W. Lawvere and M. Menni, 221-265 abstract dvi ps pdf ... Tensor products of sup-lattices and generalized sup-arrows T. Kenney and R.J. Wood, 266-287 abstract dvi ps pdf ... Lax presheaves and exponentiability Susan Niefield, 288-301

66. An ABC Of Category Theory This course is aimed at potential users of categorical ideas rather than aspiring category theorists. I will skip details wherever I can. There will not be many useful theorems in http://www.maths.gla.ac.uk/~tl/ct/

An ABC of Category Theory Autumn 2004 This course is aimed at potential users of categorical ideas rather than aspiring category theorists. I will skip details wherever I can. There will not be many useful theorems in the course. Rather, the point is to teach you how to think categorically. To this end, I will set a couple of exercises each week, and I strongly suggest that you do them: otherwise, the point is likely to be lost. (I know authors always say "the exercises are an essential part of the text", but I really think it's true here.) Informal introduction (handout, not a live performance: pdf ps ; solutions to exercises: pdf ps Categories and functors (notes: pdf ps ; solutions to exercises: pdf ps Natural transformations and equivalence (notes: pdf ps ; solutions to exercises: pdf ps Adjoints (notes: pdf ps ; solutions to exercises: pdf ps Representability (notes: pdf ps ; solutions to exercises: pdf ps Limits (notes: pdf ps ; solutions to exercises: pdf ps Adjoints, representables and limits (notes: pdf ps ; solutions to exercises: pdf ps Monads (notes: pdf ps ; solutions to exercises: pdf ps Monoidal categories (notes: pdf ps ; solutions to exercises: pdf ps Here is the page for another category theory course that I gave, more detailed than this one.

67. Front: Math.CT Category Theory Section of the e-print arXiv dealing with category theory, including such topics as enriched categories, topoi, abelian categories, monoidal categories, homological algebra. http://front.math.ucdavis.edu/math.CT

Front for the arXiv Fri, 29 Oct 2010 Front math CT search register submit journals ... iFAQ math.CT Category Theory Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 29 Oct arXiv:1010.5934 Touchard like polynomials and generalized Stirling numbers. G. Dattoli , B. Germano , M. R. Martinelli , P. E. Ricci math.CT 27 Oct arXiv:1010.5304 Note on star-autonomous comonads. Craig Pastro math.CT 26 Oct arXiv:1010.4956 Dendroidal Segal spaces and infinity-operads. Denis-Charles Cisinski , Ieke Moerdijk math.CT math.AT 26 Oct arXiv:1010.4819 On the Cohomology Comparison Theorem. Alin Stancu math.CT 22 Oct arXiv:1010.4527 Traces in monoidal categories. Stephan Stolz , Peter Teichner math.CT math.AT Cross-listings 27 Oct arXiv:1010.5397 Mirror stability conditions and SYZ conjecture for Fermat polynomials. So Okada math.AG math.CT math.RT ... math.SG Revisions 29 Oct arXiv:1009.0234 Categorical Non-standard Analysis. Hayato Saigo math.CT 29 Oct arXiv:1004.0160 Stone duality for topological theories. Dirk Hofmann , Isar Stubbe math.CT

68. Category Theory@Everything2.com A branch of mathematics I want to study one day. an extreme form of algebra. In category theory, the primitive notions are nodes and arrows. http://everything2.com/title/category theory

Near Matches Ignore Exact Everything category theory thing by rp Wed Jul 19 2000 at 13:28:08 A branch of mathematics I want to study one day. an extreme form of algebra In category theory, the primitive notions are nodes and arrows. A category is a set of nodes connected with arrows such that if a path leads from one node to another, so does a direct arrow; in other words, a transitive directed graph Nodes represent sets; arrows represent functions; categories describe particular types of sets entirely in terms of the functions that operate on them, and on related sets. This avoids the overspecification you often get when describing mathematical objects in set theoretic terms. Take a look at the definition of tuple s in terms of set That's as far as I understand it. Remind me to add to this when I finish the textbook. I like it! thing by ariels Fri Sep 01 2000 at 19:58:32 Node s do not really represent set s; this is again the overspecification that we are trying to rebel against. Nodes represent nodes. Arrow s do not represent function s, either.

69. Category Theory • Chris Waggoner • Hire Me Because I'm Smart • Mathematics Category Theory Category Theory is like Set Theory, but supposedly better. What is it, though? • It’s a collection of points, and arrows. • Unlike in Set Theory, things can http://blog.hiremebecauseimsmart.com/post/615614573/functor

70. Categories Introductory article by John Baez. http://math.ucr.edu/home/baez/categories.html

Categories, Quantization, and Much More John Baez April 12, 2006 Quantum theory can be thought of as the generalization of classical mechanics you get by dropping the assumption that observable quantities like position and momentum commute. In quantum theory one thus learns to like noncommutative, but still associative, algebras. It is interesting however to note why associativity without commutativity is studied so much more than commutativity without associativity. Basically, because most of our examples of binary operations can be interpreted as composition of functions. For example, if write simply x for the operation of adding x to a real number (where x is a real number), then x + y is just x composed with y. Composition is always associative so the + operation is associative! If we try to generalize the heck out of the concept of a group, keeping associativity as a sacred property, we get the notion of a category. Categories are some of the most basic structures in mathematics. They were created by Samuel Eilenberg and Saunders MacLane. In fact, MacLane said: "I did not invent category theory to talk about functors. I invented it to talk about natural transformations." Huh? Wait and see.

71. Category Theory Category Theory 80413/713 Fall 2010 Course Information Place PH A22 Time TR 130 - 250 Instructor Steve Awodey Office Baker 135F Office Hour Monday 1-2, or by appointment http://www.andrew.cmu.edu/course/80-413-713/

Category Theory Fall 2010 Course Information Place: PH A22 Time: TR 1:30 - 2:50 Instructor: Steve Awodey Office: Baker 135F Office Hour: Monday 1-2, or by appointment Phone: x8947 Email: awodey@andrew Secretary: Baker 135 Webpage: www.andrew.cmu.edu/course/80-413-713 Overview Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. To be followed by a Fall course on categorical logic. Prerequisites Some familiarity with abstract algebra or logic. Texts Course notes will be provided.

72. Open Problems On Model Categories Problems on model categories listed by Mark Hovey at Wesleyan University. http://claude.math.wesleyan.edu/~mhovey/problems/model.html

Model categories This is part of an algebraic topology problem list , maintained by Mark Hovey I am not sure working on model categories is a safe thing to do. It is too abstract for many people, including many of the people who will be deciding whether to hire or promote you. So maybe you should save these until you have tenure. A scheme is a generalization of a ring, in the same way that a manfold is a generalization of R^n. So maybe there is some kind of model structure on sheaves over a manifold? Presumably this is where de Rham cohomology comes from, but I don't know. It doesn't seem like homotopy theory has made much of a dent in analysis, but I think this is partly due to our lack of trying. Floer homology, quantum cohomologydo these things come from model structures? Every stable homotopy category I know of comes from a model category. Well, that used to be true, but it is no longer. Given a flat Hopf algebroid, Strickland and I have constructed a stable homotopy category of comodules over it. This clearly ought to be the homotopy category of a model structure on the category of chain complexes of comodules, but we have been unable to build such a model structure. My work with Strickland is still in progress, so you will have to contact me for details. Given a symmetric monoidal model category C, Schwede and Shipley have given conditions under which the category of monoids in C is again a model category (with underlying fibrations and weak equivalences). On the other hand, the category of commutative monoids seems to be much more subtle. It is well-known that the category of commutative differential graded algebras over Z can not be a model category with uinderlying fibrations and weak equivalences (= homology isos). On the other hand, the solution to this is also pretty well-knownyou are supposed to be using E-infinity DGAs, not commutative ones. Find a generalization of this statement. Here is how I think this should go, broken down into steps. The first step: find a model structure on the category of operads on a given model category. (Has this already been done? Charles Rezk is the person I would ask). We probably have to assume the model category is cofibrantly generated.

73. MATHS: Category Theory Category Theory. Motivation Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic. http://www.csci.csusb.edu/dick/maths/math_25_Categories.html

Skip Navigation CSUSB CNS R J Botting ... Contact ] [Search Mon Aug 11 17:01:22 PDT 2008 Contents Category Theory : Motivation : Trivial Example : Trivial Exercise ... Glossary Category Theory Motivation Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic. It is a model of a collection of things with some structural similarity. It is a comparatively recent abstraction from the various abstract algebras developed in the early part of the 20th century. The best source for detailed information is still Madc Lane's classic graduate text The original use of the term category was in the idea of a 'categorical' axiom system - an axiom system which defined its objects so exactly that all objects that satisfied the axioms were isomorphic - they mapped into each other, one-to-one, preserving all the axioms and structure. This is important, because if a logic is categorical and there exists a simple (or cheaply implemented) example then that model can become the standard and all others are handled in terms of this standard. For example binary numbers have all the properties that one can expect of objects that satisfy the rules that describe a "natural number" and are cheap to emulate using electronics. The name for such ideal systems has been changed several times in this century - categorical, free, universal, initial,... Many times category theorists have discovered that some results that they have uncovered have been discovered within a totally different area - say the theory of languages and automata. Equally often an enterprising researcher in mathematics of computer science has found that category theory allowed them to express a specific property they had observed in more general terms. The more general veiw then leads to shorter and simpler proofs of more results. This in turn often illuminates other problems.

74. Categorical Myths And Legends An archive of stories about category theorists. http://www.mcs.le.ac.uk/~ah83/cat-myths/

Categorical Myths and Legends Last updated: 5th July 2001 This site archives stories about category theorists. To search for a particular person use the Find-in-page option on the Edit menu of your web browser. Contributions and suggestions for improvement to this archive are most welcome. You can email me by clicking the button below. Stories will have to be approved by the principal characters or their close relations. title: Samuel Eilenberg author: Saunders MacLane characters: Samuel Eilenberg dates: 1914-1998 ... dates: July 2001 Author: Anne Heyworth MCS Web Maintainer Any opinions expressed on this page are those of the author. Stories linked to from this page have been approved by the people concerned.

75. Groupoid Home Page Maintained by Birant Ramazan. Address book, open problems, meetings, pictures, other resources. http://unr.edu/homepage/ramazan/groupoid/

If your browser can't read tables or if you are using a text browser, try the text-based groupoid home page Groupoid Home Page Editors: Jean Renault renault@labomath.univ-orleans.fr Arlan Ramsay ramsay@euclid.colorado.edu It was created by Arlan Ramsay Rob Chiaramonte , and Loren Woo at the University of Colorado at Boulder and is maintained by Birant Ramazan at the University of Nevada Reno New: Groupoidfest 08 , November 22-23, 2008, at UC Riverside Address book Other sources on groupoids and links Some questions on groupoids Conferences ... Some pictures Our guestbook is now operational - please feel free to browse our guestbook This page was last updated January 31 2003. ramazan@unr.edu

76. From Groups To Groupoids Notes by Ronald Brown. http://www.bangor.ac.uk/~mas010/gpds.htm

Groupoids in Mathematics the place of groupoids union with many base points From groups to groupoid s (pdf) (RB:1987) Groupoids: relating internal and external symmetry (Alan Weinstein, 1996) `Three themes in the work of Charles Ehresmann: local-to-global; groupoids; higher dimensions' (pdf) (RB: 2007), and also the books Topology and Groupoids (RB: 2006) and Categories and Groupoids (e-version) (Philip Higgins: 1971, 2005) Groupoids and crossed objects in algebraic topology pdf revised 2009 A groupoid can be described as a set G of arrows , a set O of objects , two functions s t G O called the source and target functions, and a composition function xy defined for those arrows x y such that t x s y ), with s xy s x t xy t x ). We then impose axioms of a left identity and a right identity for each arrow x, an inverse x for each x , such that s x t x t x s x ), and finally associativity. (Those who know category theory can say simply that a groupoid is a small category in which every morphism is an isomorphism.) Thus a group may be considered as a groupoid with one object. The extension from groups to groupoids starts in a formal sense with the desire to describe reversible processes which may traverse a number of states. So the group theory idea is, say, to consider a variety of journeys from say Bangor back to Bangor, whereas in groupoid theory one considers journeys between various cities in the UK, and notes that journeys can be composed if and only if the starting point of one journey is the end point of the previous one. This naive viewpoint gives rise to the heretical suggestion that

77. Category Theory - Free E-Books Category Theory list of freely downloadable books at E-Books Directory http://www.e-booksdirectory.com/listing.php?category=364

78. CT99 University of Coimbra, Portugal; 1924 July 1999. http://www.mat.uc.pt/~ct99/

79. Category Theory Authors/titles Mar 2008 Comments 21 pages. To appear in the Advances of Mathematics. Exposition improved, notion of operad with degeneracies removed as a simplification, definition of pseudo algebra http://arxiv.org/list/math.CT/0803

arXiv.org math math.CT Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Category Theory Authors and titles for math.CT in Mar 2008 [ total of 8 entries: [ showing up to 25 entries per page: fewer more arXiv:0803.0853 pdf ps other Title: Girard couples of quantales Authors: J. M. Egger David Kruml Subjects: Category Theory (math.CT) ; Logic (math.LO); Quantum Algebra (math.QA) arXiv:0803.1133 pdf ps other Title: Opposite relation on dual polar spaces and half-spin Grassmann spaces Authors: Mariusz Kwiatkowski Mark Pankov Subjects: Category Theory (math.CT) ; Group Theory (math.GR) arXiv:0803.1408 pdf ps other Title: Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras Authors: Thomas M. Fiore Po Hu Igor Kriz Comments: 21 pages. To appear in the Advances of Mathematics. Exposition improved, notion of operad with degeneracies removed as a simplification, definition of pseudo algebra improved. Subjects: Category Theory (math.CT) ; High Energy Physics - Theory (hep-th); Algebraic Topology (math.AT) arXiv:0803.2429

80. Página Do Grupo De TEORIA DAS CATEGORIAS Categories at Coimbra. Members, meetings, reports, resources. http://www.mat.uc.pt/~categ/

Members Seminars Reports Guests ... Events Universidade de Coimbra 3001-454 Coimbra PORTUGAL E-mail your comments and questions to Jorge Picado Last update: March 10, 2010

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