TY - BOOK ID - 9804043 TI - Cut elimination in categories PY - 1999 SN - 0792357205 9048152267 9401712077 PB - Dordrecht Kluwer DB - UniCat KW - Categories (Mathematics) KW - Proof theory KW - Logic, Symbolic and mathematical KW - Category theory (Mathematics) KW - Algebra, Homological KW - Algebra, Universal KW - Group theory KW - Topology KW - Functor theory KW - Proof theory. KW - Categories (Mathematics). KW - Logic. KW - Mathematical logic. KW - Category theory (Mathematics). KW - Homological algebra. KW - Computer science—Mathematics. KW - Mathematical Logic and Foundations. KW - Category Theory, Homological Algebra. KW - Symbolic and Algebraic Manipulation. KW - Homological algebra KW - Algebra, Abstract KW - Homology theory KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Mathematics KW - Metamathematics KW - Set theory KW - Syllogism KW - Argumentation KW - Deduction (Logic) KW - Deductive logic KW - Dialectic (Logic) KW - Logic, Deductive KW - Intellect KW - Philosophy KW - Psychology KW - Science KW - Reasoning KW - Thought and thinking KW - Methodology UR - https://www.unicat.be/uniCat?func=search&query=sysid:9804043 AB - 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. ER -