Articles liés à Cut Elimination in Categories

Cut Elimination in Categories - Couverture souple

Livre 2 sur 53: Trends in Logic

Dosen, K.

 
9789048152261: Cut Elimination in Categories
Couverture souple
ISBN 10 : 9048152267 ISBN 13 : 9789048152261
Editeur : Springer, 2010

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2010
Langue
anglais
ISBN 10 
9048152267
ISBN 13 
9789048152261
Reliure
Broché
Nombre de pages
244
Coordonnées du fabricant
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