Cut Elimination in Categories

K. Dosen (Autor)

Buch | Hardcover

229 Seiten

1999 | 1999 ed.
Springer (Verlag)
978-0-7923-5720-9 (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	31.5.1999
Reihe/Serie	Trends in Logic ; 6
Zusatzinfo	XII, 229 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
	Geisteswissenschaften ► Philosophie ► Logik
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-7923-5720-5 / 0792357205
ISBN-13	978-0-7923-5720-9 / 9780792357209
Zustand	Neuware