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Category Theory

Proceedings of the International Conference held in Como, Italy, July 22-28, 1990

  • Conference proceedings
  • © 1991

Overview

Editors:
  1. Aurelio Carboni
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  2. Maria Cristina Pedicchio
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  3. Guiseppe Rosolini
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1488)

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Table of contents (28 papers)

  1. Front Matter

    Pages I-VI
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  2. Some thoughts on the future of category theory

    • F. William Lawvere
    Pages 1-13

  3. What are locally generated categories?

    • Jiří Adámek, Jiří Rosický
    Pages 14-19

  4. Some remarks on free monoids in a topos

    • Jean Benabou
    Pages 20-29

  5. A generic sheaf representation for rings

    • Francis Borceux, Gilberte Van den bossche
    Pages 30-42

  6. Normalization equivalence, kernel equivalence and affine categories

    • Dominique Bourn
    Pages 43-62

  7. Computing quotients of actions of a free category

    • S. Carmody, R. F. C. Walters
    Pages 63-78

  8. A long exact sequence in non-abelian cohomology

    • Antonio M. Cegarra, Antonio R. Garzón
    Pages 79-94

  9. Algebraically complete categories

    • Peter Freyd
    Pages 95-104

  10. Order-enriched sketches for typed lambda calculi.

    • John W. Gray
    Pages 105-130

  11. First steps in synthetic domain theory

    • J. M. E. Hyland
    Pages 131-156

  12. Precategories and Galois theory

    • George Janelidze
    Pages 157-173

  13. How algebraic is the change-of-base functor?

    • George Janelidze, Walter Tholen
    Pages 174-186

  14. Fixpoint and loop constructions as colimits

    • C. Barry Jay
    Pages 187-192

  15. Preframe presentations present

    • Peter Johnstone, Steven Vickers
    Pages 193-212

  16. Strong stacks and classifying spaces

    • André Joyal, Myles Tierney
    Pages 213-236

  17. Trees in distributive categories

    • S. Kasangian, S. Vigna
    Pages 237-248

  18. A note on relations relative to a factorization system

    • G. M. Kelly
    Pages 249-261

  19. Algebras for the partial map classifier monad

    • Anders Kock
    Pages 262-278

  20. Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes

    • F. William Lawvere
    Pages 279-281
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Keywords

About this book

With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/Street (80 pp) on a growing subject: it gives an account of classical Tannaka duality in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent developments and quantum groups. No expertise in either representation theory or category theory is assumed. Topics such as the Fourier cotransform, Tannaka duality for homogeneous spaces, braided tensor categories, Yang-Baxter operators, Knot invariants and quantum groups are introduced and studies. From the Contents: P.J. Freyd: Algebraically complete categories.- J.M.E. Hyland: First steps in synthetic domain theory.- G. Janelidze, W. Tholen: How algebraic is the change-of-base functor?.- A. Joyal, R. Street: An introduction to Tannaka duality and quantum groups.- A. Joyal, M. Tierney: Strong stacks andclassifying spaces.- A. Kock: Algebras for the partial map classifier monad.- F.W. Lawvere: Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes.- S.H. Schanuel: Negative sets have Euler characteristic and dimension.-

Bibliographic Information

  • Book Title: Category Theory

  • Book Subtitle: Proceedings of the International Conference held in Como, Italy, July 22-28, 1990

  • Editors: Aurelio Carboni, Maria Cristina Pedicchio, Guiseppe Rosolini

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0084207

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54706-8Published: 23 October 1991

  • eBook ISBN: 978-3-540-46435-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 496

  • Topics: Topology, Algebraic Topology, Mathematical Logic and Foundations, Computer Science, general

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