| 書目名稱 | Cut Elimination in Categories | | 編輯 | Kosta Do?en | | 視頻video | http://file.papertrans.cn/242/241653/241653.mp4 | | 叢書名稱 | Trends in Logic | | 圖書封面 |  | | 描述 | Proof theory and category theory were first drawn together byLambek some 30 years ago but, until now, the most fundamental notionsof category theory (as opposed to their embodiments in logic) have notbeen explained systematically in terms of proof theory. Here it isshown that these notions, in particular the notion of adjunction, canbe formulated in such as way as to be characterised by compositionelimination. Among the benefits of these composition-free formulationsare syntactical and simple model-theoretical, geometrical decisionprocedures for the commuting of diagrams of arrows. Compositionelimination, in the form of Gentzen‘s cut elimination, takes incategories, and techniques inspired by Gentzen are shown to work evenbetter in a purely categorical context than in logic. An acquaintancewith the basic ideas of general proof theory is relied on only for thesake of motivation, however, and the treatment of matters related tocategories is also in general self contained. Besides familiar topics,presented in a novel, simple way, the monograph also contains newresults. It can be used as an introductory text in categorical prooftheory. | | 出版日期 | Book 1999 | | 關(guān)鍵詞 | Cut-elimination theorem; category theory; logic; proof; proof theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-1207-1 | | isbn_softcover | 978-90-481-5226-1 | | isbn_ebook | 978-94-017-1207-1Series ISSN 1572-6126 Series E-ISSN 2212-7313 | | issn_series | 1572-6126 | | copyright | Springer Science+Business Media Dordrecht 1999 |
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