Category Theory

Proceedings of the International Conference held in Como, Italy, July 22-28, 1990

Aurelio Carboni, Maria C. Pedicchio, Giuseppe Rosolini (Herausgeber)

Buch | Softcover

VIII, 496 Seiten

1991 | 1991
Springer Berlin (Verlag)
978-3-540-54706-8 (ISBN)

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With one exception, these papers are original and fullyrefereed research articles on various applications ofCategory Theory to Algebraic Topology, Logic and ComputerScience. The exception is an outstanding and lengthy surveypaper by Joyal/Street (80 pp) on a growing subject: it givesan account of classical Tannaka duality in such a way as tobe accessible to the general mathematical reader, and toprovide a key for entry to more recent developments andquantum groups. No expertise in either representation theoryor category theory is assumed. Topics such as the Fouriercotransform, Tannaka duality for homogeneous spaces, braidedtensor categories, Yang-Baxter operators, Knot invariantsand quantum groups are introduced and studies.From the Contents: P.J. Freyd: Algebraically completecategories.- J.M.E. Hyland: First steps in synthetic domaintheory.- G. Janelidze, W. Tholen: How algebraic is thechange-of-base functor?.- A. Joyal, R. Street: Anintroduction to Tannaka duality and quantum groups.- A.Joyal, M. Tierney: Strong stacks andclassifying spaces.- A.Kock: Algebras for the partial map classifier monad.- F.W.Lawvere: Intrinsic co-Heyting boundaries and the Leibnizrule in certain toposes.- S.H. Schanuel: Negative sets haveEuler characteristic and dimension.-

Some thoughts on the future of category theory.- What are locally generated categories?.- Some remarks on free monoids in a topos.- A generic sheaf representation for rings.- Normalization equivalence, kernel equivalence and affine categories.- Computing quotients of actions of a free category.- A long exact sequence in non-abelian cohomology.- Algebraically complete categories.- Order-enriched sketches for typed lambda calculi..- First steps in synthetic domain theory.- Precategories and Galois theory.- How algebraic is the change-of-base functor?.- Fixpoint and loop constructions as colimits.- Preframe presentations present.- Strong stacks and classifying spaces.- Trees in distributive categories.- A note on relations relative to a factorization system.- Algebras for the partial map classifier monad.- Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes.- Concretely functorial programming.- Weak products over a locally Hausdorff locale.- Categorical interpolation: Descent and the Beck-Chevalley condition without direct images.- An n-categorical pasting theorem.- Topos-theoretic approaches to modality.- Negative sets have Euler characteristic and dimension.- Modular categories.- Some constructive results related to compactness and the (strong) Hausdorff property for locales.- An introduction to Tannaka duality and quantum groups.

Erscheint lt. Verlag	23.10.1991
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 496 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	754 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
Schlagworte	algebraic topology • categories • category theory • Euler characteristic • Homotopy • Knot invariant • Model of Computations • Sheaves • Topoi
ISBN-10	3-540-54706-1 / 3540547061
ISBN-13	978-3-540-54706-8 / 9783540547068
Zustand	Neuware