Exponentiable Functors Between Quantaloid-Enriched Categories |
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| Authors: | Maria Manuel Clementino Dirk Hofmann Isar Stubbe |
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| Institution: | (1) Centro de Matemática, Universidade de Coimbra, Coimbra, Portugal;(2) Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal;(3) Research Foundation Flanders (FWO), Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium |
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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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| Keywords: | Quantaloid Enriched category Exponentiability Partial product |
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