Trends in Logic

By: K. Dosen

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Hardcover | 31 May 1999

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248 Pages

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24.13 x 16.51 x 1.91

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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.

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Mathematical Foundation Mathematical Logic Algebra Geometry Algebraic Geometry Philosophy Philosophy & Logic Computing & I.T.Databases

Data Capture & Analysis Computer Science Mathematical Theory of Computation Maths for Computer Scientists

Preface
Introduction	p. 1
Categories	p. 17
Functors	p. 53
Natural Transformations	p. 70
Adjunctions	p. 81
Comonads	p. 149
Cartesian Categories	p. 195
Conclusion	p. 219
References	p. 221
Index	p. 225
Table of Contents provided by Blackwell. All Rights Reserved.

Trends in Logic

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