Cut Elimination in Categories

K. Dosen (Autor)

Buch | Softcover

229 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1999
Springer (Verlag)
978-90-481-5226-1 (ISBN)

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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.

2. Functors.- 3. Natural Transformations.- 4. Adjunctions.- 5. Comonads.- 6. Cartesian Categories.- Conclusion.- References.

Erscheint lt. Verlag	9.12.2010
Reihe/Serie	Trends in Logic ; 6
Zusatzinfo	XII, 229 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Geisteswissenschaften ► Philosophie ► Logik
	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	90-481-5226-7 / 9048152267
ISBN-13	978-90-481-5226-1 / 9789048152261
Zustand	Neuware