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Cut Elimination in Categories

  • Book
  • © 1999

Overview

Authors:
  1. Kosta Došen

    1. University of Toulouse III, Toulouse, France
      Mathematical Institute, Belgrade, Yugoslavia

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Part of the book series: Trends in Logic (TREN, volume 6)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Kosta Došen
    Pages 1-16

  3. Categories

    • Kosta Došen
    Pages 17-52

  4. Functors

    • Kosta Došen
    Pages 53-69

  5. Natural Transformations

    • Kosta Došen
    Pages 70-80

  6. Adjunctions

    • Kosta Došen
    Pages 81-148

  7. Comonads

    • Kosta Došen
    Pages 149-194

  8. Cartesian Categories

    • Kosta Došen
    Pages 195-218

  9. Conclusion

    • Kosta Došen
    Pages 219-220

  10. Back Matter

    Pages 221-229
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Keywords

About this book

Proof theory and category theory were first drawn together by Lambek some 30 years ago but, until now, the most fundamental notions of category theory (as opposed to their embodiments in logic) have not been explained systematically in terms of proof theory. Here it is shown that these notions, in particular the notion of adjunction, can be formulated in such as way as to be characterised by composition elimination. Among the benefits of these composition-free formulations are syntactical and simple model-theoretical, geometrical decision procedures for the commuting of diagrams of arrows. Composition elimination, in the form of Gentzen's cut elimination, takes in categories, and techniques inspired by Gentzen are shown to work even better in a purely categorical context than in logic. An acquaintance with the basic ideas of general proof theory is relied on only for the sake of motivation, however, and the treatment of matters related to categories is also in general self contained. Besides familiar topics, presented in a novel, simple way, the monograph also contains new results. It can be used as an introductory text in categorical proof theory.

Authors and Affiliations

  • University of Toulouse III, Toulouse, France

    Kosta Došen

  • Mathematical Institute, Belgrade, Yugoslavia

    Kosta Došen

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