---

＜電子ブック＞
Cut Elimination in Categories / by K. Dosen
(Trends in Logic, Studia Logica Library. ISSN:22127313 ; 6)

版	1st ed. 1999.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1999
本文言語	英語
大きさ	XII, 229 p : online resource
著者標目	*Dosen, K author SpringerLink (Online service)
件　名	LCSH:Logic LCSH:Mathematical logic LCSH:Algebra, Homological LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Logic FREE:Mathematical Logic and Foundations FREE:Category Theory, Homological Algebra FREE:Symbolic and Algebraic Manipulation
一般注記	2. Functors -- 3. Natural Transformations -- 4. Adjunctions -- 5. Comonads -- 6. Cartesian Categories -- Conclusion -- References 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 HTTP:URL=https://doi.org/10.1007/978-94-017-1207-1

 類似資料