Category Theory

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.-