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Exponentiable Functors Between Quantaloid-Enriched Categories

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Abstract

Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s exponentiability follows from the works of Niefield (J. Pure Appl. Algebra 23:147–167, 1982) and Dyckhoff and Tholen (J. Pure Appl. Algebra 49:103–116, 1987).

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Authors and Affiliations

  1. Centro de Matemática, Universidade de Coimbra, Coimbra, Portugal

    Maria Manuel Clementino

  2. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    Dirk Hofmann

  3. Research Foundation Flanders (FWO), Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    Isar Stubbe

Authors
  1. Maria Manuel Clementino
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  2. Dirk Hofmann
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  3. Isar Stubbe
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Correspondence to Isar Stubbe.

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Clementino, M.M., Hofmann, D. & Stubbe, I. Exponentiable Functors Between Quantaloid-Enriched Categories. Appl Categor Struct 17, 91–101 (2009). https://doi.org/10.1007/s10485-007-9104-5

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  • DOI: https://doi.org/10.1007/s10485-007-9104-5

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