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Full Description
With one exception, these papers are original and fully
refereed research articles on various applications of
Category Theory to Algebraic Topology, Logic and Computer
Science. The exception is an outstanding and lengthy survey
paper by Joyal/Street (80 pp) on a growing subject: it gives
an account of classical Tannaka duality in such a way as to
be accessible to the general mathematical reader, and to
provide a key for entry to more recent developments and
quantum groups. No expertise in either representation theory
or category theory is assumed. Topics such as the Fourier
cotransform, Tannaka duality for homogeneous spaces, braided
tensor categories, Yang-Baxter operators, Knot invariants
and quantum groups are introduced and studies.
From the Contents: P.J. Freyd: Algebraically complete
categories.- J.M.E. Hyland: First steps in synthetic domain
theory.- G. Janelidze, W. Tholen: How algebraic is the
change-of-base functor?.- A. Joyal, R. Street: An
introduction 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 Leibniz
rule in certain toposes.- S.H. Schanuel: Negative sets have
Euler characteristic and dimension.-
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.
