Re: Inductive datatypes in toposes

[Luigi Santocanale <santocan@labri.fr>]

Lutz Schroeder a écrit :
> 
> Dear categorists,
> 
> 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:
\x1f
@incollection {MR81f:18019,
    AUTHOR = {Johnstone, Peter T. and Wraith, Gavin C.},
     TITLE = {Algebraic theories in toposes},
 BOOKTITLE = {Indexed categories and their applications},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {661},
     PAGES = {141--242},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1978},
   MRCLASS = {18B25 (18C10)},
  MRNUMBER = {81f:18019},
}

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

For a subtopos structure:

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

Best,

	Luigi

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