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Monoidal categories with natural numbers object

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Abstract

The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness of the concept.

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Authors and Affiliations

  1. Department of Mathematics Statistics and Computing Sciences, Dalhousie University, B3H 3J5, Halifax, NS, Canada

    Robert Paré & Leopoldo Román

  2. Instituto de Matemátics, Universidad Nacional Autonoma de México, 04510, Mexico, D.F.

    Robert Paré & Leopoldo Román

Authors
  1. Robert Paré
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  2. Leopoldo Román
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Additional information

This work was partially carried out while both authors were guests of McGill University and while the second author was a guest of Dalhousie University. Both authors acknowledge support from the Natural Sciences and Engineering Research Council of Canada and the Québec Department of Education.

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Paré, R., Román, L. Monoidal categories with natural numbers object. Stud Logica 48, 361–376 (1989). https://doi.org/10.1007/BF00370829

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  • DOI: https://doi.org/10.1007/BF00370829

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