{"product_id":"cut-elimination-in-categories-von-k-dosen","title":"Cut Elimination in Categories","description":"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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792357209\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048152261\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792357209","offer_id":50827308998,"sku":"9780792357209","price":160.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048152261","offer_id":39415587405917,"sku":"9789048152261","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/70a38d43-72ff-4b78-8d8a-2ec0bdc92298.jpg?v=1772262743","url":"https:\/\/shop.autorenwelt.de\/en\/products\/cut-elimination-in-categories-von-k-dosen","provider":"Autorenwelt Shop","version":"1.0","type":"link"}