JOURNAL OF PURE AND APPLIED ALGEBRA VOLUME 116 - 1997 Special volume on the occasion of the 60th birthday of Professor Peter J. Freyd Guest editor: P.T. Johnstone NORTH-HOLLAND Amsterdam — Lausanne — New York — Oxford —- Shannon — Tokyo JOURNAL OF PURE AND APPLIED ALGEBRA VOLUME 116, NUMBERS 1-3, 28 MARCH 1997 Special volume on the occasion of the 60th birthday of Professor Peter J. Freyd CONTENTS Editorial J. Adamek and J. Rosicky Finite models of sketches B. Banaschewski and C.J. Mulvey A constructive proof of the Stone—Weierstrass theorem R. Betti Adjointness in descent theory R.F. Blute, J.R.B. Cockett and R.A.G. Seely Categories for computation in context and unified logic M. Bunge and |. Moerdijk On the construction of the Grothendieck fundamental group of a topos by paths P. Dehornoy Groups with a complemented presentation 115 A.D. Elmendorf and J.P. May Algebras over equivariant sphere spectra 139 M.P. Fiore and G. Rosolini Two models of synthetic domain theory 151 H. Hu and J.W. Pelletier On regular monomorphisms in weakly locally presentable categories 163 C.B. Jay Finite objects in a locos 169 M. Jibladze A presentation of the initial lift-algebra 185 P. Johnstone Cartesian monads on toposes 199 J. Lambek Relations in operational categories 221 J.-P. Olivier and D. Serrato Peirce allegories. Identities involving transitive elements and symmetrical ones 249 J. van Oosten The modified realizability topos 273 F. Piessens and E. Steegmans Proving semantical equivalence of data specifications 291 C. Townsend Localic Priestley duality 323 Author Index