Description
Springer Category Theory Proceedings Of The International Conference Held In Como Italy July 22-28 1990 1991 Edition by Aurelio Carboni Maria C. Pedicchio Giuseppe Rosolini
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.- Table of contents : 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.