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Cut Elimination in Categories : Trends in Logic - Kosta Dosen

Cut Elimination in Categories

Trends in Logic

Hardcover Published: 31st May 1999
ISBN: 9780792357209
Number Of Pages: 229

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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.

Preface
Introductionp. 1
Categoriesp. 17
Functorsp. 53
Natural Transformationsp. 70
Adjunctionsp. 81
Comonadsp. 149
Cartesian Categoriesp. 195
Conclusionp. 219
Referencesp. 221
Indexp. 225
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792357209
ISBN-10: 0792357205
Series: Trends in Logic
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 229
Published: 31st May 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 1.16