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From: Luigi Santocanale <santocan@labri.fr>
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Subject: Re: Inductive datatypes in toposes
Date: Mon, 03 Mar 2003 17:23:38 +0100
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Lutz Schroeder a =E9crit :
>=20
> Dear categorists,
>=20
> is there a good reference for the construction of inductive datatypes
> (lists, trees etc.) in a topos with nno (assuming that my guess that
> such a construction is indeed possible is correct)?

Here are those I know:
=1F
@incollection {MR81f:18019,
    AUTHOR =3D {Johnstone, Peter T. and Wraith, Gavin C.},
     TITLE =3D {Algebraic theories in toposes},
 BOOKTITLE =3D {Indexed categories and their applications},
    SERIES =3D {Lecture Notes in Math.},
    VOLUME =3D {661},
     PAGES =3D {141--242},
 PUBLISHER =3D {Springer},
   ADDRESS =3D {Berlin},
      YEAR =3D {1978},
   MRCLASS =3D {18B25 (18C10)},
  MRNUMBER =3D {81f:18019},
}

@article {MR48:8597,
    AUTHOR =3D {Lesaffre, Brigitte},
     TITLE =3D {Structures alg\'ebriques dans les topos \'el\'ementaires}=
,
   JOURNAL =3D {C. R. Acad. Sci. Paris S\'er. A-B},
    VOLUME =3D {277},
      YEAR =3D {1973},
     PAGES =3D {A663--A666},
   MRCLASS =3D {18C10 (02H10)},
  MRNUMBER =3D {48 \#8597},
MRREVIEWER =3D {Andreas Blass},
}

For a subtopos structure:

@incollection {MR95h:68133,
    AUTHOR =3D {Jay, C. Barry and Cockett, J. R. B.},
     TITLE =3D {Shapely types and shape polymorphism},
 BOOKTITLE =3D {Programming languages and systems---ESOP '94 (Edinburgh,
              1994)},
    SERIES =3D {Lecture Notes in Comput. Sci.},
    VOLUME =3D {788},
     PAGES =3D {302--316},
 PUBLISHER =3D {Springer},
   ADDRESS =3D {Berlin},
      YEAR =3D {1994},
   MRCLASS =3D {68Q65 (68N15)},
  MRNUMBER =3D {95h:68133},
}

Best,

	Luigi

--=20
Luigi Santocanale
http://www.labri.fr/~santocan/