As category theory approaches its first half-century, it continues to grow, finding new applications in areas that would have seemed inconceivable a generation ago, as well as in more traditional areas. The language, ideas, and techniques of category theory are well suited to discovering unifying structures in apparently different contexts. Representing this diversity of the field, this book contains the proceedings of an international conference on category theory. The subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for nonexperts to get a feel for the diversity of current applications of category theory.

Titles in this series are copublished with the Canadian Mathematical Society. Members of the Canadian Mathematical Society may order at the AMS member price.

Readership

Graduate students or postgraduate researchers in category theory or in any of the fields which use categorical techniques and ideas.

Table of Contents

• A. Bagchi -- DeMorgan's law and related identities in classifying topoi
• B. Banaschewski and A. Pultr -- A Stone duality for metric spaces
• R. Betti -- Sheaves in cocomplete categories
• D. Bourn -- Low dimensional geometry of the notion of choice
• M. Bunge -- Classifying toposes and fundamental localic groupoids
• A. Carboni, M. C. Pedicchio, and N. Pirovano -- Internal graphs and internal groupoids in Mal'cev categories
• G. Castellini, J. Koslowski, and G. E. Strecker -- Hereditary and modal closure operators
• H. A. Chen and P. H. Chu -- What is a Gabriel topology over a graded ring?
• J. R. B. Cockett and D. Spencer -- Strong categorical datatypes I
• Y. Diers -- The Zariski category of graded commutative rings
• R. C. Flagg -- Completeness in continuity spaces
• K. A. Hardie and K. H. Kamps -- Variations on a theme of Dold
• H. Hu -- Dualities for accessible categories
• J. Isbell -- Some problems in descriptive locale theory
• J. F. Jardine -- Modelling homotopy coherence
• G. Jarzembski -- Elementary reflections of concrete categories of mixed structures
• M. Johnson and S.-H. Sun -- Remarks on representations of universal algebras by sheaves of quotient algebras
• V. Lyubashenko -- Categorical aspects of conformal field theory
• S. Mac Lane -- Coherence theorems and conformal field theory
• S. Majid -- Braided groups and duals of monoidal categories
• C. J. Mulvey and J. W. Pelletier -- A quantisation of the calculus of relations
• D. Pavlović -- A logical view on the adjoint functor theorem
• G. Richter -- Axiomatizing algebraically behaved categories of Hausdorff spaces
• R. Rosebrugh and R. J. Wood -- Relational databases and indexed categories
• K. I. Rosenthal -- Linear indexed quantales and quantalic hyperdoctrines
• M. Sobral and W. Tholen -- Effective descent morphisms and effective equivalence relations
• V. Trnková -- Functorial selection of morphisms