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         System Theory:     more books (100)
  1. Linear System Theory: The State Space Approach by Lotfi A. Zadeh, Charles A. Desoer, 2008-07-24
  2. Search Games and Other Applications of Game Theory by Andrey Garnaev, 2000-06-15
  3. Uncertainty-Based Information: Elements of Generalized Information Theory (Studies in Fuzziness and Soft Computing) by George J. Klir, Mark J. Wierman, 1999-11-23
  4. Career Development and Systems Theory: A New Relationship by Wendy Patton, Mary McMahon, 1998-05-20
  5. Emergence in Complex Cognitive, Social and Biological Systems
  6. Theories and Systems of Psychology by Robert W. Lundin, 1996
  7. Theories of Counseling and Psychotherapy: Systems, Strategies, and Skills (3rd Edition) by Linda W. Seligman, Lourie W. Reichenberg, 2009-08-09
  8. Statistical Thermodynamics and Stochastic Theory of Nonlinear Systems Far from Equilibrium (Advanced Series in Statistical Mechanics) by Werner Ebeling, Igor M. Sokolov, 2005-10-30
  9. Sociology and the New Systems Theory: Toward a Theoretical Synthesis by Kenneth D. Bailey, 1994-01
  10. Cybernetics and Systems Theory in Management: Tools, Views, and Advancements by Steven E. Wallis, 2009-12-31
  11. Linear Matrix Inequalities in System and Control Theory (Studies in Applied and Numerical Mathematics) by Stephen Boyd, Laurent El Ghaoui, et all 1997-06-26
  12. Geometric Theory of Discrete Nonautonomous Dynamical Systems (Lecture Notes in Mathematics) by Christian Pötzsche, 2010-09-17
  13. Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness (Texts in Applied Mathematics) by Diederich Hinrichsen, Anthony J. Pritchard, 2010-02-09
  14. General Systems Theory by Lars Skyttner, 2001-06-15

81. Passive And Active Vibration Isolation Systems - Theory
The passive vibration isolation system consists of a spring and damper (dashpot) The active system uses also accelerometers and electromagnetic drivers
http://physics.nad.ru/Physics/English/spri_txt.htm
PASSIVE AND ACTIVE VIBRATION ISOLATION SYSTEMS Vibrations accompany us everywhere and in most cases these vibrations are undesirable. First of all we can mention the vibration of cars and carriages, motors and machine tools, oil and gas platforms, buildings and constructions in a zone of seismic activity, undesirable vibrations of laboratory tables (especially optical), setups, etc. In all these cases an object has to be isolated from the source of vibrations. Despite of all constructional distinctions the essence of vibration isolation systems are identical. The passive vibration isolation system consists of a spring and damper (dash-pot). The spring is intended to soften vibrations and pushes, and damper has to terminate the oscillation which is excited in system. The active system uses also accelerometers and electromagnetic drivers which allows higher degree of vibration isolation to be achieved. Let us consider the work of passive vibration isolation system by the example of a suspension bracket of the automobile. In any suspension bracket there are elastic elements, which soften pushes and impacts of the road. Other not less important element of a suspension bracket is the shock-absorber the device which is intended to terminate excited the oscillation. Many drivers think that shock-absorbers is only the means to maintain comfort. Actually functions of this element of a suspension bracket are directly connected to maintenance of contact of a wheel with road, i.e. with controllability of the automobile and traffic safety.

82. Bio Mimetic Control Research Center Homepage
Topics include biological control systems, motor system control theory, biologically integrative sensors, and environment adaptive robotic systems. Site in English and Japanese.
http://www.bmc.riken.go.jp/index_en.html
Bio-Mimetic Control Research Center
Japanese RIKEN (The Institute of Physical and Chemical Research) at Nagoya
2271-130, Anagahora, Shimoshidami, Moriyama-ku Nagoya, 463-0003 JAPAN Our snake-like swimming robot using an artificial muscle is introduced
by mass media. (March 4, 2005)
General Invitation of Postdoctoral Researcher and Technical Stafa BMC Access Guide The aim of research into bio-mimetic control is to mimic the highly sophisticated control functions of the living systems in order to create flexible, precise and reliable engineering systems. The Bio-Mimetic Control Research Center (BMC) of RIKEN was established in October 1993 as a two-term project for the purpose of carrying out research in this highly interdisciplinary endeavor. The second term of research, begun in October 2001, will further promote work from such aspects as system control theory, robotics, biological control and sensory mechanisms.
BMC is located in the Nagoya area, itself situated in an area of Japan possessed of a long tradition in such highly sophisticated manufacturing industries as aircraft and automobile manufacture. It is expected that the advanced research potential possessed by RIKEN fused with the special characteristics of the region will bear much fruit toward advancing the aims of bio-mimetic research.

83. A Curriculum For Cybernetics And Systems Theory
List of suggested books, periodicals, television shows and computer programs for a classroom curriculum or individual study in cybernetics and systems theory.
http://www.well.com/user/abs/curriculum.html
A Curriculum for Cybernetics and Systems Theory
Alan B. Scrivener
abs@well.com

FIRST DRAFT
(c) 1 March 1990 by Alan Scrivener
SECOND DRAFT
(c) 22 August 2002 by Alan Scrivener
New! Beginning in September 2002, I will be sharing a free e-Zine, "Cybernetics in the Third Millenium" (C3M), about 1,000 - 10,000 words per issue and about one isssue per month. If you are interested in a free subscription to this electronic newsletter, please email abs@well.com with C3M in the subject.
CONTENTS
INTRODUCTION
What This Is
This is a list, with reviews, of suggested books, periodicals, television shows and computer programs for a classroom curriculum or individual study in cybernetics and systems theory. It does not (yet) include a course plan, glossary, or extended bibliography. I was asked to write this by some teachers who received a copy of class notes I prepared for a course in "Understanding Whole Systems" sixteen years ago at the University of California at Santa Cruz. They asked how I would revise it based on what I know today. This document answers that question. [A similar web site exists at the Principia Cybernetica Project . - ABS 8/11/96]
Cybernetics and Systems Theory Defined
Right off, let's dispense with the childish belief that words "have" meanings. Charles Dodson / Lewis Carroll was close to the mark with this dialogue between Alice and Humpty Dumpty:

84. Systems
Systems theory Group.
http://www.ladseb.pd.cnr.it/control/control.html
The Systems Theory Group at ISIB-information
(former LADSEB-CNR)
Contents
  • Personnel Research areas Collaborations EU Projects ... Publications
  • 1. Personnel
    The personnel is of two kinds: permanent staff at ISIB (research scientists) and people holding positions at the University who have ongoing research activities at ISIB (collaborators). Permanent staff
      Lorenzo Finesso Andrea Gombani Stefano Secchi External collaborators (Professors at the University of Padova)
        Giovanni Di Masi Michele Pavon Giorgio Picci Stefano Pinzoni Wolfgang Runggaldier
        2. Research areas
        The Systems Theory group has been active since 1974.
        Research at ISIB-information (previously LADSEB) can be framed in five areas: realization and approximation of stochastic systems, stochastic control, nonlinear filtering, mathematical finance, modelling and performance analysis of communication protocols for industrial applications. Stochastic realization Stochastic control : approximation techniques have been studied for problems of stochastic control with partial observations. In particular, using transformation measure techniques, there have been obtained approximate problems whose almost optimal solutions are in fact almost optimal for the original problem as well, with error arbitrar ily small (see e.g. Bensoussan and Runggaldier [1987], Di Masi and Runggaldier [1987], Runggaldier and Zane [1991], Runggaldier and Stettner [1991]. Recently, the connections between piecewise linear control systems and adaptive controllers have been studied, with the pourpose of showing the relevance of adaptive techniques for the control of nonlinear systems. In Albertini and Runggaldier [1988] Fleming's logarithmic transform has been extended to the discrete case.

    85. Cybernetics And Systems Theory
    The following links provide general background information on the field of Cybernetics and Systems theory, an interdisciplinary academic domain.
    http://pespmc1.vub.ac.be/CYBSYSTH.html
    Cybernetics and Systems Theory
    The following links provide general background information on the field of Cybernetics and Systems Theory , an interdisciplinary academic domain. This material was collected and is provided in the context of the Principia Cybernetica Project , but can be consulted independently of the rest of the project. Although there are relatively few research centers and even fewer educational programs devoted to the domain, a lot of activity is going on in between established departments. This is shown by the number of associations , conferences and journals active in the domain. The best way of getting acquainted with the main ideas of cybernetics and systems theory is to read a few of the classic books or papers defining the domain. Some of these books are freely available through our Principia Cybernetica library . Other, specific bibliographic references can be found in the library database of the Department of Medical Cybernetics and AI at the University of Vienna. There also exists more general reference material , including our own Web Dictionary of basic concepts.

    86. What Is Systems Theory?
    Systems theory the transdisciplinary study of the abstract organization of phenomena, independent of their substance, type, or spatial or temporal scale of
    http://pespmc1.vub.ac.be/SYSTHEOR.html
    What is Systems Theory?
    Systems Theory : the transdisciplinary study of the abstract organization of phenomena, independent of their substance, type, or spatial or temporal scale of existence. It investigates both the principles common to all complex entities, and the (usually mathematical) models which can be used to describe them. Systems theory was proposed in the 1940's by the biologist Ludwig von Bertalanffy : General Systems Theory, 1968 ), and furthered by Ross Ashby Introduction to Cybernetics The developments of systems theory are diverse (Klir, Facets of Systems Science , 1991), including conceptual foundations and philosophy (e.g. the philosophies of Bunge, Bahm and Laszlo); mathematical modeling and information theory (e.g. the work of Mesarovic and Klir ); and practical applications. Mathematical systems theory arose from the development of isomorphies between the models of electrical circuits and other systems. Applications include engineering, computing, ecology, management, and family psychotherapy. Systems analysis, developed independently of systems theory, applies systems principles to aid a decisIon-maker with problems of identifying, reconstructing, optimizing, and controlling a system (usually a socio-technical organization), while taking into account multiple objectives, constraint s and resources. It aims to specify possible courses of action, together with their risks, costs and benefits. Systems theory is closely connected to

    87. Complex Systems, Systems Theory, Sociotechnical Systems, Self-Adaptive Systems,
    This web site explores how Chaos theory and the Science of Complexity relate to the thinking about Organizations as dynamic, selfevolving complex systems.
    http://www.brint.com/Systems.htm
    About BRINT News About BRINT Contact Us Advertise Here Welcome to the World's No. 1 Resource for Business Technology Management and Knowledge Management
    Knowledge Management Common Body of Knowledge
    KM-CBK ) Release 1.0
    Services Knowledge Portals Knowledge Map Knowledge Network Book of Knowledge
    Channels General Business Business Technology E-Business Knowledge Management
    Community Join the Network! Community Events Executive Jobs
    Resources News World Information! Conferences ... Books
    SEARCH HELP
    Organizations as Self-Adaptive Complex Systems
    Subject Portals

    Systems Thinking
    Complex Systems Chaos Theory Systems Dynamics ... Artificial Life Link Directories
    Systems Thinking
    Complex Systems Chaos Theory Systems Dynamics ... Artificial Life More Articles and Research Papers For many more articles and research papers, click on the subject specific research sources below. You will find hundreds of articles on the subject areas of this page with always updated links in the most relevant sources. Prior version of this page with links "Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." Jame Gleick in Chaos: Making A New Science See above 'Subject Portals' and 'Link Directories' for other subject specific research sites.

    88. The Control Systems Group
    Membership organization dedicated to application of William T. Powers' perceptual control theory model to understanding purposeful behavior.
    http://www.ed.uiuc.edu/csg/
    The Control Systems Group website has moved to www.perceptualcontroltheory.org

    89. Cybernetics, Systems Theory, And Complexity
    (Francis Heylighen); What is Systems theory? (Francis Heylighen); What is Complexity? (Francis Heylighen); Origins of Cybernetics (Stuart Umpleby)
    http://carbon.cudenver.edu/~mryder/itc_data/complexity.html
    Martin Ryder
    University of Colorado at Denver
    School of Education
    Cybernetics, Systems Theory and Complexity
    related pages: Second-Order Cybernetics memetics Corollary Sources
    Some Basics
    Resources
    Readings
    • Bollen (1995) Adaptive Hypertext Networks
  • Geyer (1994) The Challenge of Sociocybernetics
  • Francis Heylighen
  • Kevin Kelly
  • Kelly interview (F. Scott Taylor, 1995)
  • 90. Signals, Systems And Control Demonstrations
    Resource of applets and interactive lectures dedicated the control theory from the Johns Hopkins University.
    http://www.jhu.edu/~signals/
    Johns
    Hopkins
    University Signals
    Systems
    Control
    Joy of Convolution

    A Java applet that performs graphical convolution of continuous-time signals on the screen. Select from provided signals, or draw a signal with the mouse. Includes an audio introduction with suggested exercises and a multiple-choice quiz. ( Prepared by Steven Crutchfield, Fall 1996.) Joy of Convolution (Discrete Time)
    A Java applet that performs graphical convolution of discrete-time signals on the screen. Select from provided signals, or draw a signal with the mouse. Includes an audio introduction with suggested exercises and a multiple-choice quiz. ( Original applet by Steven Crutchfield, Summer 1997, is available here . Update by Michael Ross , Fall, 2001.) Interactive Lecture Module: Continuous-Time LTI Systems and Convolution
    A combination of Java Script, RealAudio, technical presentation on the screen, and Java applets that is used at Johns Hopkins to complement classroom lectures on the discrete-time case. ( Applets by Steven Crutchfield, interface by Mark Nesky, Spring 1998.)

    91. Systems Theory - Wikipedia, The Free Encyclopedia
    Systems theory or systemics is an interdisciplinary field which studies relationships of Modern systems theory was founded by Ludwig von Bertalanffy,
    http://en.wikipedia.org/wiki/Systems_theory
    Systems theory
    From Wikipedia, the free encyclopedia.
    Systems theory or systemics is an interdisciplinary field which studies relationships of systems as a whole. Modern systems theory was founded by Ludwig von Bertalanffy William Ross Ashby and others between the and the on principles from philosophy, physics biology and engineering and later grew into numerous fields including philosophy sociology organizational theory management ... psychotherapy (within family systems therapy ) and economics among others. Cybernetics is a closely related field. In recent times complex systems has increasingly been used as a synonym. TIMELINE
    • cybernetics (W. Ross Ashby, Norbert Wiener) Mathematical theory of the communication and control of systems through regulatory feedback. Closely related: " control theory 1950 General Systems Theory (founded by Ludwig von Bertalanffy) catastrophe theory (Ren© Thom, E.C. Zeeman) Branch of mathematics that deals with bifurcations in dynamical systems, classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances. chaos theory (David Ruelle, Edward Lorenz, Mitchell Feigenbaum, Steve Smale, James A. Yorke) Mathematical theory of nonlinear dynamical systems that describes bifurcations, strange attractors, and chaotic motions.

    92. Climate Dynamics,Chaos And Quantum Mechanics
    Explains a general systems theory for chaos, quantum mechanics and gravity as applied to weather patterns. Includes illustrations, scientific publications and references.
    http://www.geocities.com/CapeCanaveral/Lab/5833/
    MIRROR SITE http://members.tripod.com/~amselvam: A General Systems Theory of Everything from Chaos, Quantum Mechanics and Gravity Applicable to Dynamical Systems of all Space-Time Scales from Subatomic Dynamics of Quantum Systems to Macro-Scale Fluid Flows
    who are the visitors? View Page Stats

    See who's visiting this page. Updated on 7 June 2005
    Sign Guestbook
    View Guestbook Fractals: The beautiful complex patterns generated by simple iterative computations: Some examples
    A hierarchy of selfsimilar structures: The large scale is a magnified version of the small scale.
    A Theory of Everything for Chaos,Quantum Mechanics and Gravity, Applicable to Macroscale Weather Patterns
    A superstring theory for atmospheric flow dynamics?
    For a brief summary GO TO Universal quantification for self-organized criticality in atmospheric flows
    and
    CHAOS, QUANTUMLIKE MECHANICS AND NON-LOCALITY IN ATMOSPHERIC FLOWS

    For detailed theory GO TO Table of Contents
    A Superstring Theory for Fractal Spacetime,Chaos and Quantumlike Mechanics in Atmospheric Flows
    by A.M.SELVAM and SUVARNA FADNAVIS

    93. Optimization And Systems Theory At KTH
    What is optimization and systems theory? in Mathematical Systems theory and Optimization (Photos ). * Center for Autonomous Systems
    http://www.optsyst.math.kth.se/

    Search
    Sitemap Contact
    Optimization and Systems Theory
    ...
    Student information
    (in Swedish)
    Second Chinese-Swedish Control Conference
    First Swedish-Israeli Control Conference
    Final program
    First Swedish-Chinese Control Conference
    ...
    weboptsyst@math.kth.se

    94. Peter Benner - Software
    SLICOT Subroutine Library in Control theory, Parallel Library in Control (PLiC) for largescale time-invariant linear control systems in state-space form on parallel distributed computers, eigenvalues of Hamiltonian Matrices, subroutines for compressing a symmetric or triangular matrix to packed storage mode or to unpack a packed array to full storage mode, benchmark examples of discrete-time algebraic Riccati equations, benchmark examples of continuous-time algebraic Riccati equations.
    http://www.math.tu-berlin.de/~benner/Software/index_de.html
    Peter Benner - Software
    The software retrievable from this page is usually archived in tar files that are compressed with gzip . If you have any problems downloading or uncompressing the files, please click here
    Fortran 77
    HAPACK
    Maintained and developed by Peter Benner and
    HAPACK is an LAPACK-style software package for Hamiltonian and skew-Hamiltonian matrices. It provides subroutines for computing eigenvalues, eigenvectors, and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices, as well as structured Schur forms and several orthogonal symplectic factorizations of such matrices. Mex files and Matlab interfaces are vailable as well, see also Matlab software below.
    PLiCMR
    Maintained and developed by
    The Parallel Library in Control: Model Reduction (PLiCMR) package contains subroutines for model reduction of linear dynamical systems in state-space form on parallel distributed computers. Currently it contains routines for balanced truncation, singular perturbation approximation, optimal Hankel norm approximation, and stochastic balancing for stable systems using dense matrix algebra. The parallelization model is based on the approach used in ScaLAPACK . Numerical computations are based on ScaLAPACK as far as possible and communication is performed using the Basic Linear Algebra Communication Subroutines (BLACS) on top of a communication library such as PVM or MPI.

    95. Climate Dynamics,Chaos And Quantum Mechanics
    A general systems theory for chaos, quantum mechanics and climate dynamics applicable to dynamical systems of all spacetime scales.
    http://www.geocities.com/amselvam
    MIRROR SITE http://members.tripod.com/~amselvam: A General Systems Theory of Everything from Chaos, Quantum Mechanics and Gravity Applicable to Dynamical Systems of all Space-Time Scales from Subatomic Dynamics of Quantum Systems to Macro-Scale Fluid Flows
    who are the visitors? View Page Stats

    See who's visiting this page. Updated on 7 June 2005
    Sign Guestbook
    View Guestbook Fractals: The beautiful complex patterns generated by simple iterative computations: Some examples
    A hierarchy of selfsimilar structures: The large scale is a magnified version of the small scale.
    A Theory of Everything for Chaos,Quantum Mechanics and Gravity, Applicable to Macroscale Weather Patterns
    A superstring theory for atmospheric flow dynamics?
    For a brief summary GO TO Universal quantification for self-organized criticality in atmospheric flows
    and
    CHAOS, QUANTUMLIKE MECHANICS AND NON-LOCALITY IN ATMOSPHERIC FLOWS

    For detailed theory GO TO Table of Contents
    A Superstring Theory for Fractal Spacetime,Chaos and Quantumlike Mechanics in Atmospheric Flows
    by A.M.SELVAM and SUVARNA FADNAVIS

    96. Videotape Systems Theory
    This page is a brief discussion of videotape systems theory, with some history thrown in for good measure. It may help give you an idea of why early
    http://www.lionlmb.org/quad/theory.html
    Videotape Systems Theory
    This page is a brief discussion of videotape systems theory, with some history thrown in for good measure. It may help give you an idea of why early videotape machines sometimes weighed upwards of a ton, and were so finicky. It also gives you some idea of what engineers had to overcome to build a machine the average person could afford!
    General update 10-19-2004. Email address updated. Status of D-VHS updated.
    Table of contents
    Videotape Systems Theory
    A Little History first! Any discussion of videotape theory would be incomplete without a brief description of the events that led to the development of the videotape recorder. As you will come to appreciate from reading this tutorial, the development of a practical videotape machine was no trivial task. The videotape machine represents perhaps, the most amazing combination of mechanical and electronic engineering that you will ever find in one device. Indeed, technology developed for the videotape machine also is fundamental to the now ubiqutious computer disk drive as well. The first stirrings that led to a practical videotape machine happened in 1951. This is not to say that there was considerable interest in the concept of recording TV pictures before that. Indeed, ever since Jack Mullin had demonstrated practical magnetic audio recording in this country (Using two tape recorders captured from the Germans during World War II), there was also an interest in recording television pictures. (You will read later why this was so problematic.) In any case, the audio tape recorder had given life to a postwar Ampex Corporation, who was looking for a product to manufacture after it's government contract to manufacture radar components had been canceled.

    97. Neural Information Processing Systems (NIPS)
    2003, December 813, Vancouver, Canada. Neural computation, learning theory, algorithms and architectures, neuroscience, vision, speech, control and diverse applications. Submission deadline 6 June 2003.
    http://www-2.cs.cmu.edu/~nips/

    The NIPS home page has been moved to www.nips.snl.salk.edu. Click here.

    The NIPS home page has been moved to www.nips.snl.salk.edu. Click here.

    98. Chapter 4: Introduction To Systems Theory
    CHAPTER 4 Introduction to Systems theory. (a). Humans and Their Models. (b). Definitions of Systems and Models. (c). Structure of Systems
    http://www.physicalgeography.net/fundamentals/chapter4.html
    FUNDAMENTALS OF PHYSICAL GEOGRAPHY HOME FUNDAMENTALS
    ONLINE TEXTBOOK
    GLOSSARY ... ABOUT FUNDAMENTALS OF PHYSICAL GEOGRAPHY CHAPTER 4: Introduction to Systems Theory (a). Humans and Their Models (b). Definitions of Systems and Models (c). Structure of Systems (d). Environmental Systems as Energy Systems (e). Food Chain as an Example of a System (f). Equilibrium Concepts and Feedbacks Study Guide Additional Readings Internet Weblinks Created by Dr. Michael Pidwirny, University of British Columbia - Okanagan Email Corrections and Suggestions to: user = "michael.pidwirny"; site = "ubc.ca"; document.write(''); document.write(user + '@' + site + ''); // End > Powered by Mac OS X and Webstar V

    99. Whole Systems
    Cybernetics and Systems theory (200+) Principia Cybernetica General Semantics Ludwig von Bertalanffy - General Systems theory
    http://www.worldtrans.org/whole.html
    This area is devoted to the study of whole systems. Nature is a whole system. But also an economy, a family, a company, a community, or many other things, can be looked at as whole systems. A whole system view would include all the factors involved and examine how they relate to each other and how they work as a whole. To deal with a whole system we can't leave anything out as irrelevant. Intuition is as important as rationality, we must address both scientific and artistic approaches, both material and spritual needs, the small as well as the big, what we feel as well as what we think, what we perceive as well as what we imagine. Whole systems are dynamic, they change they move, they develop. Frozen pictures of how things are supposed to be might do us no good, we need to deal with the live systems, whichever surprising directions that might take us in. There is no one authority in the field of whole systems. Luckily nobody has monopolized it by putting it into a standard curriculum defining what it IS. So, we all have the opportunity to discover together what whole systems are about. There is a Whole Systems mailing list for the exploration of whole systems principles, particularly in regards to economic, ecological, sociological and metaphysical transformation of our civilization.

    100. Category Theory
    JeanPierre Marquis of the University of Montreal introduces the general mathematical theory of structures and systems of structures.
    http://plato.stanford.edu/entries/category-theory/
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    Category Theory
    1. General Definitions, Examples and Applications
    defined as sets, category theory cannot provide a philosophically enlightening foundation for mathematics. In terms of collections, a category C can be described as a collection Ob , the objects of C , which satisfy the following conditions: For every pair a b of objects, there is a collection Mor a b ), namely, the morphisms from a to b in C (when f is a morphism from a to b , we write f a b For every triple a b and c of objects, there is a partial operation from pairs of morphisms in Mor a b ) X Mor b c ) to morphisms in Mor a c ), called the composition of morphisms in

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