1. Categorical Logic Borceux, F. Handbook of categorical algebra (Encyclopedia of Mathematics and its Applications). Makkai, M.\ and Reyes, G. FirstOrder categorical logic. http://www.andrew.cmu.edu/user/awodey/catlog/

Categorical Logic Fall 2002 Course Information Instructor: Steve Awodey Office: Baker 152 (mail: Baker 135) Office Hour: Thursday 1-2, or by appointment Phone: 8947 Email: awodey@andrew Secretary: Baker 135 Overview This course focuses on applications of category theory in logic and computer science. A leading idea is functorial semantics, according to which a model of a logical theory is a set-valued functor on a structured category determined by the theory. This gives rise to a syntax-invariant notion of a theory and introduces many algebraic methods into logic, leading naturally to the universal and other general models that distinguish functorial from classical semantics. Such categorical models occur, for example, in denotational semantics. In this connection the lambda-calculus is treated via the theory of cartesian closed categories. Similarly higher-order logic is modelled by the categorical notion of a topos. Using sheaves, topos theory also subsumes Kripke semantics for intuitionistic logic. Prerequisites 80-413/713 Category Theory, or equivalent.

2. Wesleyan Research Areas type theory, linear logic, categorical logic, and relation of mathematics, modeltheoretic algebra. of Mathematics Mathematical logic, applications of model http://www.math.wesleyan.edu/research-areas.htm

Faculty, Staff, and Graduate Students Undergrad Math Program Seminars and Colloquia Graduate Program ... Alphabetical Listing of Faculty with Research Interests Research areas of the department: Algebra Analysis Computer Science Discrete Mathematics ... Topology There are weekly seminars in most of the above areas as well as a regular departmental colloquium series and a weekly graduate-student-run lunchtime seminar. Algebra Wai Kiu Chan , Ph.D. Ohio State University Assistant Professor of Mathematics Number theory, quadratic forms Karen L. Collins , Ph.D. MIT Professor of Mathematics Algebraic and enumerative combinatorics, graph theory W. Wistar Comfort , Ph.D. Washington (Seattle) Professor of Mathematics Point-set topology, ultrafilters, set theory, topological groups Anthony W. Hager , Ph.D. Penn State Professor of Mathematics Lattice-ordered algebraic structures, general and categorical topology

3. Graduate Mathematics And Computer Science Program algebraic topology, analysis of algorithms, categorical algebra, combinatorics, complex analysis, computational logic, data mining, ergodic theory, geometric http://www.math.wesleyan.edu/graduate.htm

Faculty, Staff, and Graduate Students Undergrad Math Program Seminars and Colloquia Graduate Program ... Contact Us Graduate Program Programs of Study Courses Research Areas Facilities ... More Information The Department's graduate programs include a Ph. D. program in mathematics and M. A. programs in mathematics and in computer science. The research emphasis at Wesleyan is in pure mathematics and theoretical computer science. One of the distinctive features of our department is the close interaction between the computer science faculty and the mathematics faculty, particularly those in logic and discrete mathematics. Among possible fields of specialization for Ph.D. candidates are algebraic topology, analysis of algorithms, categorical algebra, combinatorics, complex analysis, computational logic, data mining, ergodic theory, geometric analysis, general topology, graph theory, homological algebra, Kleinian groups and discrete groups, lattice-ordered algebraic structures, logic programming, mathematical physics, model theory, model-theoretic algebra, number theory, operator algebras, probability theory, proof theory, topological dynamics, and topological groups. http://www.math-cs.wesleyan.edu

4. 22M:330 Fall 2004 - Topics In Algebra - Categorical Structures & Applications Edward N. Zalta (ed.); Mac Lane, Saunders Categories in geometry, algebra and logic . Math. Japon. 42 (1995) 1, 169178. categorical structures are http://www.math.uiowa.edu/~fsouza/22M330-F04/Announcement2pt2.html

22M:330:001 - Fall 2004 - Course Announcement v. 2.2 TOPICS IN ALGEBRA Categorical Structures and Applications SHORTCUTS: Aims Audience Bibliography Goals ... Topics This is a very preliminary syllabus. Your constructive criticism is greatly appreciated ! Feel free to address any questions and concerns to the instructor. Thank you in advance ! LECTURE SCHEDULE: Currently, M W F 3:30-4:20 p.m. The instructor received a proposal to change the time to 2:30-3:20 p.m. (assuming that there is a room available), and would greatly appreciate receiving information from all the interested students about their time availability (2:30, 3:30, or 4:30), time preference(s), and area(s) of interest. INTENDED AUDIENCE: Mathematics students interested in being exposed to topics from various areas within the same framework, observing similarities between them; Mathematics students who intend to specialize in any of the following areas: Algebra , more especifically: Various algebraic structures, including Clifford, Hopf, Lie, and operator algebras; their representation theories; their generalizations to various categories (e.g. graded algebras); quantum algebra; Foundations of mathematics , especially category theory, logic, and models of computation;

5. A Geometric And Algebraic View Of MHC-peptide Complexes And Their define two types of categorical variables of the MHCpeptide the use of propositional logic, and by making a geometric We conclude that algebra and geometry provide a convenient http://rdre1.inktomi.com/click?u=http://www.pubmedcentral.gov/articlerender.fcgi

6. Introduction Lambek continued his work in ring theory and categorical algebra (often in There then followed a fruitful collaboration on categorical logic with P. Scott http://www.math.mcgill.ca/triples/lambek97/lamintro.html

Introduction to MSCS volume This volume is dedicated to our friend, colleague, and teacher Joachim (Jim) Lambek. On December 5,1997, a small conference was held at McGill on the occasion of Jim Lambek's 75th birthday. Subsequently it was decided to publish two volumes of papers contributed in his honour to mark this occasion; this issue of Mathematical Structures in Computer Science is one of the volumes, the other is Volume 6 of the journal Theory and Applications of Categories . At the December 1997 conference, a brief biographical essay was presented by Michael Barr; that essay appears in the TAC volume. But we wish to make some further remarks here. Jim completed his Ph.D. at McGill under Hans Zassenhaus in 1950, and has remained at McGill since then. But it is of interest to note that Jim wrote two theses: the second involved biquaternions in mathematical physics, and so forshadows a significant feature of his career: Jim has consistently shown a remarkable range of interests, from physics to linguistics, from algebra to logic, from the history and philosophy of mathematics to the theory of computing science (although he never touches a computer, to this day!). Let us just review a small sample of his more than 100 published papers. In the mid 1960's Lambek became increasingly interested in category theory. His first monograph, "Completions of Categories" (Springer LNM

7. TUD : ACTUAL RESEARCH REPORT - Group 1. Algebra And Logic - Mathematical Logic A logic (with proof theory, recursion theory and model theory) this involves constructive type theory, categorical logic, universal algebra, domain theory http://www.tu-darmstadt.de/forschung/bericht/040100.en.tud

ACTUAL RESEARCH REPORT Group 1. Algebra and Logic - Mathematical Logic and Foundations of Computer Science Foreword by the President Tips for users Departments of the TUD Collaborative research centers ... Research homepage Full text search: Quick search in research report Advanced search in research report Advanced search in bibliography Contact: Arbeitsgruppe 1, Fachbereich Mathematik, Technische Universität Schlossgartenstraße 7 64289 Darmstadt Tel.: +49-6151-16-4686 Fax: +49-6151-16-3317 Building/Room: S2 15 / 206 E-mail: Internet: www.mathematik.tu-darmstadt.de/ags/ag1/Sekretariat/sekretariat_de.html Description of the Institute: Algebra and Logic - Mathematical Logic and Foundations of Computer Science Faculty: Klaus Keimel Ulrich Kohlenbach Martin Otto Thomas Streicher ... Thomas Ihringer Retired: Peter Burmeister Rudolf Wille The research group primarily represents the subject area of Mathematical Logic viewed as an applied foundational discipline between mathematics and computer science . Research activities focus on the application of proof theoretic, recursion theoretic, category theoretic, algebraic and model theoretic methods from mathematical logic to mathematics and computer science. Beside classical mathematical logic (with proof theory, recursion theory and model theory) this involves constructive type theory, categorical logic, universal algebra, domain theory, lattice theory, finite model theory, and algorithmic issues.

8. Subject Classification Lecture Notes in Pure and Applied algebra 180 181 and Education, The Bulletin of Symbolic logic, vol categorical Dynamics in Proceedings of Aarhus May 1978 Open http://www.acsu.buffalo.edu/~wlawvere/subject.html

F. William Lawvere Subject Classification of Articles HOME Chronological list Functorial Semantics of Algebraic Theories Proceedings of the National Academy of Science 50 , No. 5 (November 1963), 869-872. Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models ; North-Holland, Amsterdam (1965), 413-418. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories Springer Lecture Notes in Mathematics No. 61 , Springer-Verlag (1968), 41-61. Review of P. M. Cohn's Universal Algebra , 2nd Edition, American Scientist (May-June 1982), p. 329. 42. with J. Adamek and J. Rosicky, How algebraic is algebra? Theory and Applications of Categories (2001) 253-283 (electronic). 44. with J. Adamek and J. Rosicky: On the duality between varieties and algebraic theories, Algebra Universalis, Topos Theory Quantifiers and Sheaves Proceedings of the International Congress on Mathematics , (Nice 1970), Gauthier-Villars (1971) 329-334. Introduction to the Proceedings of the Halifax Conference, Toposes, Algebraic Geometry and Logic Springer Lecture Notes in Mathematics No. 274

9. Guests Of The Algebra And Logic Group At The University Of Saskatchewan the strict refinement property) in terms of certain formulas (hformulas) defined by E. A. Palyutin in categorical Horn classes, I. algebra and logic 19(1980 http://math.usask.ca/fvk/alggtalk.htm

ALGEBRA AND LOGIC GROUP of the Mathematical Sciences Group University of Saskatchewan 106 Wiggins Road Saskatoon, SK, S7N 5E6, Canada Phone: (306) 966-6081 - Fax: (306) 966-6086 Past Talks of Our Guests Friday, November 19, 1997, 4:00 p.m. Professor Sibylla Priess-Crampe gave a talk in the Department Colloquium on Fixed Point and Coincidence Theorems for Ultrametric Spaces Abstract: An ultrametric space (X,d,G) is a set X with an ultrametric distance functions d from X to G , where G is a partially ordered set with a smallest element 0. d has the same properties as a metric but instead of the triangle inequality the following one: For all g of G , if d(x,y) and d(y,z) are at most g then also d(x,z) is at most g . A special role for ultrametric spaces play spherically complete ultrametric spaces. "Sperically complete" corresponds to the property "maximal valued" for valued fields. For spherically complete ultrametric spaces there holds a fixed point theorem which looks like Banach's fixed point theorem for metric spaces. One has furthermore a generalization of this singlevalued fixed point theorem to multivalued mappings (again as it is the case in the metric situation). Some hints to applications of the theorems will be given. Friday, February 13, 1998, 4:00 p.m.

10. Science And Math - Geometry contains online books and research papers on categorical geometry and categorical algebra. logical Art and the Art of logic learn about pentominoes and what http://www.information-entertainment.com/ScienceMath/Geometry.html

Please show your support for this site and visit the sponsors Science And Math - Geometry Geometry is more than about measuring angles and circles or anything to do with shapes. Although that is a big part of this subject, there is a key to how they relate to real life use. The key is logic. You might think that you only need this logic when building things, but you can use this skill of deductive reasoning in everyday life. Geometry has a basic set of postulates and theories. You must have them memorized and understand those principles before you can move too far into this subject. Once you get a grip on them, you must be able to reason how you get from point A to point Z using those principles. This is where your skills of logic come in. It is not merely a matter to accept the final result, but to understand the process of coming from the beginning to the end. Engineers and scientists will need Geometry in their professional fields. All students who plan to enter college need this skill to graduate. For them, it is mandatory to learn this subject. For everyone else, the ability to think in a logical manner will save you from making a lot of wrong choices. Geometry will help you get there.

11. 1Up Science > Links Directory > Math: Geometry: Algebraic Geometry Online books and research papers on categorical algebra, categorical logic, categorical geometry, lattice theory, universal algebra and algebraic geometry. http://www.1upscience.com/links/geometry-algebraic-geometry.html

Home Contact Us Privacy Search 1Up Science Science A-Z A B C D ... Z Agriculture Animals Economics Farming Practices Field Crops ... More.. Alternative Science Alchemy Archaeology Astronomy Cryptozoology ... More.. Astronomy Astrophysics Calendars and Timekeeping Cosmology Eclipses and Occultations ... More.. Biology Biochemistry Biotechnology Botany Ecology ... More.. Chemistry Biochemistry Chemical Engineering Electrochemistry Elements ... More.. Earth Sciences Ecology Geology Geomatics Geophysics ... More.. Environment Air Quality Ecology Energy Health ... More.. Math Algebra Chaos and Fractals Differential Equations Geometry ... More.. Physics Alternative Astronomy Astrophysics Crystallography ... More.. Social Sciences Anthropology Archaeology Cognitive Science Economics ... Urban and Regional Planning s More.. Technology Acoustics Aerospace Chemical Engineering Electronics ... Geometry : Algebraic Geometry Description Categories Events Research Groups Software Elliptic curves See Related Categories Science: Math: Number Theory Sites AGATHOS - Algebraic Geometry: A Total Hypertext Online System AGATHOS is a hypertext-based, online system for learning algebraic geometry developed while teaching a year-long graduate class at the University of Maryland in College Park. The most important assumption is that the reader has completed a year-long graduate course in abstract algebra.

12. Algebra And Logic In Computer Science Group - Department Of Computing Science algebra and logic in Computer Science Group Non used to provide a basis for categorical unification in Symposium on MultipleValued logic (ISMVL 2001), May 22-24 http://www.cs.umu.se/~peklund/groupsonweb/al/al_mon.htm

Algebra and Logic in Computer Science Group Non-classical logic, generalised terms, and unification Unification in non-classical logics, with various approaches to handling generalised terms, has drawn more and more attention in recent years. It turns out to be among the most promising areas of research on non-classical logics and its applications. Composition of monads provides a method for extending the notion of terms. Variable substitutions, viewed as morphisms in the corresponding Kleisli categories over composed monads, correspond to variables being assigned to various generalised power sets of terms. These techniques for monad compositions are used to provide a basis for categorical unification in the framework of generalised terms. Monads have shown to be useful in different fields related to computer science. In functional programming monad compositions are applied to structuring of functional programs. In particular, in functional programs like parsers or type checkers the monad needed is often a composed monad. Collaborators: Patrik Eklund Selected papers: Electronic Notes in Theoretical Computer Science 40 (2001) Department of Computing Science Umeå university The information on this page was last checked 2002-03-20 magalan@cs.umu.se

13. Yoogoo - Your Best Archive Online books and research papers on categorical algebra, categorical logic, categorical geometry, lattice theory, universal algebra and algebraic geometry. http://www.yoogoo.com/Top/Science/Math/Geometry/Algebraic_Geometry

your personal directory of the internet. Top Science Math Geometry See also: AGATHOS - Algebraic Geometry: A Total Hypertext Online System - An online system for learning algebraic geometry. Algebraic Curves - An overview. Algebraic Functions and Projective Curves - Home page of the book by David Goldschmidt. Full text (registration required), errata, discussion forum. Algebraic Geometry - Links and list of algebraic geometers. Algebraic Geometry Notebooks for Non-Experts - By Aksel Sogstad. Short introductory sketch of some topics in the algebraic geometry of curves. ArXiv Front - Algebraic Geometry - Papers and preprints. Borcherds' Solutions to Hartshorne - Solutions to the exercises in chapter 1 of Hartshorne's "Algebraic Geometry" Categorical Geometry Homepage - Online books and research papers on categorical algebra, categorical logic, categorical geometry, lattice theory, universal algebra and algebraic geometry. Computations in Algebraic Geometry with Macaulay 2 - Edited by David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels. Full text in DVI, PS and PDF. Differential Algebraic Geometry - A Scheme-theoretic Approach - Slides in multimedia format from a lecture by Henri Gillet at MSRI.

14. Yoogoo - Your Best Archive Homepage This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical geometry, lattice theory http://www.yoogoo.com/Top/Science/Math/Algebra/Category_Theory

your personal directory of the internet. Top Science Math Algebra ... Journals See also: Ccard A Gentle Introduction to Category Theory - Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few) examples are taken from algorithmics. The text is a long PostScript file. Applied and Computational Category Theory - A brief description of category theory, and some useful links. 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. Categorical Geometry Homepage - This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical geometry, lattice theory, universal algebra, algebraic geometry. Categorical Myths and Legends - An archive of stories about category theorists. Categories Home Page - Web page for the category theory mailing list. Categories, Quantization, and Much More

15. George Voutsadakis Research Interests. algebraic logic; categorical and Universal algebra; Ordered Structures; Combinatorics; Theoretical Computer Science. Mathematical Genealogy. http://pigozzi.lssu.edu/www/RESEARCH/papers.html

George Voutsadakis Assistant Professor School of Mathematics and Computer Science Lake Superior State University Research Interests Algebraic Logic Categorical and Universal Algebra Ordered Structures Combinatorics Theoretical Computer Science Mathematical Genealogy Technical Reports On Some Operations on Classes of Algebras and Coalgebras from a Bialgebraic Viewpoint pdf or postscript Probablistic Threshold Agent Networks pdf or postscript The Categories of Finitary Binary Functions and Finite Automata Networks pdf or postscript On the Categorical Mobius Calculus pdf or postscript Universal Bialgebra: Unifying Universal Algebra and Coalgebra pdf or postscript Combinatorial Analysis of the State Space Structure of Finite Automata Networks pdf or postscript Preprints Algebraic Logic Categorical Abstract Algebraic Logic: Gentzen pi-institutions and the deduction-detachment property pdf or postscript Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients

16. About "Categorical Geometry" well as to the online book categorical Geometry. Books, research papers, and notes on categorical algebra, logic, and geometry. http://mathforum.org/library/view/8173.html

Categorical Geometry Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.geometry.net/cg/ Author: Zhaohua Luo Description: See a brief tour of categorical geometry, which studies the geometric properties of unitary categories. The categorical approach to algebraic geometry was initiated by Yves Diers in his pioneer book Categories of Commutative Algebras (Oxford University Press, 1992). This site contains papers and notes written by Zhaohua Luo on this subject since 1992. Many of the new concepts and results described are influenced by Diers's book, to which the reader is referred for details, as well as to the online book Categorical Geometry. Books, research papers, and notes on categorical algebra, logic, and geometry. Levels: College Research Languages: English Resource Types: Articles Books Math Topics: Algebraic Geometry Home The Math Library Quick Reference ... Contact Us http://mathforum.org/

17. PUT Libary 13. Borceux, Francis, Handbook of categorical algebra Vol. 16. de Queiroz, Ruy JGB, logic for Concurrency and Synchronisation, 2003, Michal. 17. http://www.ii.uib.no/~wolter/put/put-library.html

PUT Libary Nr. Authors/Editors Title Year Place Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 1 - Background: Mathematical Structures Uwe Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 2 - Background: Computational Structures Michal Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 4 - Semantic Modelling Michal Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 5 - Logic and Algebraic Methods Uwe van Leeuwen, Jan Handbook of Theoretical Computer Science Vol. A - Algorithms and Complexity Uwe van Leeuwen, Jan Handbook of Theoretical Computer Science Vol. B - Formal Models and Semantics Uwe Rozenberg/ Salomaa Handbook of Formal Languages Vol. 1 - Word, Language, Grammar Uwe Rozenberg/ Salomaa Handbook of Formal Languages Vol. 2 - Linear Modeling: Background and Application Uwe Robinson/ Voronkov Handbook of Automated Reasoning Vol. 1 Uwe Robinson/ Voronkov Handbook of Automated Reasoning Vol. 2 Uwe Borceux, Francis Handbook of Categorical Algebra Vol. 1

18. Cours Functoriality. Naturality. Monoidal categories. categorical logic. Hopf algebra. Linear logic. MAT3341, Applied Linear algebra Vector and matrix norms. http://aix1.uottawa.ca/~epaqu045/cours.html

Cours Suivis Directed studies: Quantum Groups Hopf algebra. Quantum plane and its symmetries. The lie algebra SL(2). The enveloping of sl (2). Hopf algebra Structure on U q sl (2)). Yang-Baxter equation and (co)braided bialgebras. Drinfeld's quantum double. Serminar: Quantum Computing Basics of quantum mechanics. Quantum states. Quantum entanglement and decoherence. Classical and quantum information theory. Quantum computations. Quantum cryptography. Shor's algorithm for fast factorisation. Mathematical Logic Propositional and predicate logic. Syntax and semantics of formal systems. Saturation theorems. Incompleteness and undecidability theorems. Special topics in mathematics: Introduction to category theory and categorical logic Introduction to category theory. Functoriality. Naturality. Monoidal categories. Categorical logic. Hopf algebra. Linear logic. Applied Linear Algebra Vector and matrix norms. Schur canonical form, QR, LU, Cholesky and singular value decomposition, generalized inverses, Jordan form, Cayley-Hamilton theorem, matrix analysis and matrix exponentials, eigenvalue estimation and the Greshgorin Circle Theorem; quadratic forms, Rayleigh and minima principles. The theoretical and numerical aspects will be studied.

19. Wauu.DE: Science: Math: Algebra: Category Theory Geometry Homepage This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical geometry, lattice http://www.wauu.de/Science/Math/Algebra/Category_Theory/

Home Science Math Algebra : Category Theory Search DMOZ-Verzeichnis: All Categories Categories Onlye Kategorien: Events Journals Research Groups Links: A Gentle Introduction to Category Theory Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few) examples are taken from algorithmics. The text is a long PostScript file. http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html Applied and Computational Category Theory A brief description of category theory, and some useful links. http://www.risc.uni-linz.ac.at/research/category/ Categorical Geometry Homepage This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical geometry, lattice theory, universal algebra, algebraic geometry. http://www.geometry.net/cg/index.html Categorical Myths and Legends An archive of stories about category theorists. http://www.mcs.le.ac.uk/~ah83/cat-myths/ Categories Home Page Web page for the category theory mailing list.

20. Transactions Of The American Mathematical Society MR 87g08022. 15. E. Palyutin. The description of categorical quasivarieties. algebra and logic, 1486111, 1975. MR 532672. 16. Á. Szendrei. http://www.ams.org/tran/1998-350-01/S0002-9947-98-01594-3/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6850 (e) ISSN 0002-9947 (p) Previous issue Table of contents Next issue Articles in press ... All issues Minimal sets and varieties Author(s): Keith A. Kearnes; Emil W. Kiss; Matthew A. Valeriote Journal: Trans. Amer. Math. Soc. MSC (1991): Primary 08A05; Secondary 08A40, 08B15 Retrieve article in: PDF DVI TeX PostScript This article is available free of charge Abstract References Similar articles Additional information Abstract: The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable. References: J. Berman and S. Seif. An approach to tame congruence theory via subtraces.

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