Applied Categorical Structures

, Volume 17, Issue 1, pp 91–101 | Cite as

Exponentiable Functors Between Quantaloid-Enriched Categories

  • Maria Manuel Clementino
  • Dirk Hofmann
  • Isar Stubbe
Article

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).

Keywords

Quantaloid Enriched category Exponentiability Partial product 

Mathematics Subject Classifications (2000)

06F07 18A22 18D05 18D20 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Maria Manuel Clementino
    • 1
  • Dirk Hofmann
    • 2
  • Isar Stubbe
    • 3
  1. 1.Centro de MatemáticaUniversidade de CoimbraCoimbraPortugal
  2. 2.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  3. 3.Research Foundation Flanders (FWO), Department of Mathematics and Computer ScienceUniversity of AntwerpAntwerpBelgium

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