Cut Elimination in Categories

Cut Elimination in Categories

3 (1 rating by Goodreads)
By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 4 business days
When will my order arrive?

Description

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.
show more

Product details

  • Hardback | 229 pages
  • 162.6 x 233.7 x 22.9mm | 498.96g
  • Dordrecht, Netherlands
  • English
  • 1999 ed.
  • XII, 229 p.
  • 0792357205
  • 9780792357209

Table of contents

Preface. Introduction. 1. Categories. 2. Functors. 3. Natural Transformations. 4. Adjunctions. 5. Comonads. 6. Cartesian Categories. Conclusion. References. Index.
show more

Rating details

1 ratings
3 out of 5 stars
5 0% (0)
4 0% (0)
3 100% (1)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X