Category Theory: Proceedings of the International Conference held in Como, Italy, July 22–28, 1990

F. William Lawvere (auth.), Aurelio Carboni, Maria Cristina Pedicchio, Guiseppe Rosolini (eds.)3540547061, 0387547061

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.-

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Table of contents :
Some thoughts on the future of category theory….Pages 1-13
What are locally generated categories?….Pages 14-19
Some remarks on free monoids in a topos….Pages 20-29
A generic sheaf representation for rings….Pages 30-42
Normalization equivalence, kernel equivalence and affine categories….Pages 43-62
Computing quotients of actions of a free category….Pages 63-78
A long exact sequence in non-abelian cohomology….Pages 79-94
Algebraically complete categories….Pages 95-104
Order-enriched sketches for typed lambda calculi…..Pages 105-130
First steps in synthetic domain theory….Pages 131-156
Precategories and Galois theory….Pages 157-173
How algebraic is the change-of-base functor?….Pages 174-186
Fixpoint and loop constructions as colimits….Pages 187-192
Preframe presentations present….Pages 193-212
Strong stacks and classifying spaces….Pages 213-236
Trees in distributive categories….Pages 237-248
A note on relations relative to a factorization system….Pages 249-261
Algebras for the partial map classifier monad….Pages 262-278
Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes….Pages 279-281
Concretely functorial programming….Pages 282-297
Weak products over a locally Hausdorff locale….Pages 298-305
Categorical interpolation: Descent and the Beck-Chevalley condition without direct images….Pages 306-325
An n-categorical pasting theorem….Pages 326-358
Topos-theoretic approaches to modality….Pages 359-378
Negative sets have Euler characteristic and dimension….Pages 379-385
Modular categories….Pages 386-400
Some constructive results related to compactness and the (strong) Hausdorff property for locales….Pages 401-409
An introduction to Tannaka duality and quantum groups….Pages 413-492