Notre Dame Journal of Formal Logic

Book Review: Colin McLarty. Elementary Categories, Elementary Toposes.

Jean-Pierre Marquis

Article information

Notre Dame J. Formal Logic, Volume 39, Number 3 (1998), 436-445.

First available in Project Euclid: 6 December 2002

Permanent link to this document

Digital Object Identifier


Marquis, Jean-Pierre. Book Review: Colin McLarty. Elementary Categories, Elementary Toposes. Notre Dame J. Formal Logic 39 (1998), no. 3, 436--445. doi:10.1305/ndjfl/1039182256.

Export citation


  • Barr, M., and C. Wells, Category Theory for Computing Science, Prentice Hall, London, 1990. MR 92g:18001
  • Bell, J. L., Toposes and Local Set Theories: An Introduction, Oxford University Press, Oxford, 1988. Zbl 0649.18004 MR 90e:18002
  • Fiore, M., Axiomatic Domain Theory in Categories of Partial Maps, Cambridge University Press, Cambridge, 1996. Zbl 0979.68549 MR 98c:68127
  • Fiore, M., and G. Rosolini, “Two models of synthetic domain theory,” Journal of Pure and Applied Algebra, vol. 116 (1996), pp. 151–62. Zbl 0879.18007 MR 98j:18003
  • Fiore, M., A. Juang, et al., “Domains and denotational semantics: History, accomplishments and open problems,” Bulletin of the EATCS, vol. 59 (1996), pp. 227–56.
  • Goldblatt, R., Topoi: The Categorical Analysis of Logic, North-Holland, Amsterdam, 1979. Zbl 0434.03050 MR 81a:03063
  • Hyland, M., “First steps in synthetic domain theory,” pp. 131–56 in Category Theory: Como 1990, edited by A. Carboni, M. C. Pedicchio, and G. Rosolini, LNM 1488, Springer-Verlag, Berlin, 1991. Zbl 0747.18004 MR93g:68075
  • Johnstone, P., Topos Theory, Academic Press, London, 1977. Zbl 0368.18001 MR 57:9791
  • Joyal, A., and I. Moerdijk, Algebraic Set Theory, Cambridge University Press, Cambridge, 1995. Zbl 0847.03025 MR 96k:03127
  • Lawvere, W., and S. Schanuel, Conceptual Mathematics, Cambridge University Press, Cambridge, 1997. Zbl 0889.18001 MR 99e:18001
  • Lawvere, W., ed., Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, no. 274, Springer-Verlag, Berlin. Zbl 0233.00005 MR 48:8592
  • MacLane, S., and I. Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer-Verlag, Berlin, 1992. Zbl 0822.18001 MR 96c:03119
  • Makkai, M., “Avoiding the axiom of choice in general category theory,” Journal of Pure and Applied Algebra, vol. 108 (1996), pp. 109–73. Zbl 0859.18001 MR 97h:18002
  • Makkai, M., “Generalized sketches as a framework for completeness theorems,” Journal of Pure and Applied Algebra, vol. 115 (1997), pp. 49–79(Part I), 179–212(Part II), and 241–74(Part III). Zbl 0871.03045 MR 98a:03105
  • Makkai, M., and G. Reyes, “Completeness theorems for intuitionistic and modal logic in a categorical setting,” Annals of Pure and Applied Logic, vol. 72 (1995), pp. 25–101. Zbl 0830.03036 MR 96b:03087
  • McLarty, C., “The uses and abuses of the history of topos theory,” British Journal of the Philosophy of Science, vol. 41 (1990), pp. 351–75. Zbl 0709.18002 MR 92b:01044
  • Reyes, G., and H. Zolfaghari, “Bi-Heyting algebras, toposes and modalities,” Journal of Philosophical Logic, vol. 25 (1996), pp. 25–43. Zbl 0851.03022 MR 97d:03020
  • Rosolini, G., “Notes on synthetic domain theory,”, 1997.
  • Taylor, P., “The fixed-point property in synthetic domain theory,” pp. 152–60 in Sixth Symposium on Logic in Computer Science, IEEE Computer Society Press, Amsterdam, 1996.