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Cut Elimination in Categories (Trends in Logic, 6) by Došen, Kosta is a nonfiction available to read on EtoBox.

What is Cut Elimination in Categories (Trends in Logic, 6) about?

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. Erscheinungsdatum: 09.12.2010

Who reads Cut Elimination in Categories (Trends in Logic, 6)?

Author

Došen, Kosta

Publisher

Springer Netherlands

Published

2008

Language

EN

ISBN

9789401712071

Category

nonfiction

Subjects

Philosophy, Mathematics, Humanities