Cut Elimination in Categories

1. Auflage. Softcover version of original hardcover Auflage 1999
ISBN: 978-90-481-5226-1
Verlag: Springer Netherlands

Buch, Englisch, Band 6, 229 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 376 g

Reihe: Trends in Logic

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.

Zielgruppe

Research

Autoren/Hrsg.

Dosen, K.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

2. Functors.- 3. Natural Transformations.- 4. Adjunctions.- 5. Comonads.- 6. Cartesian Categories.- Conclusion.- References.