Isar Stubbe; Dirk Hofmann; Maria Manuel Clementino;
Exponentiable Functors Between Quantaloid-Enriched Categories
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).
Applied Categorical Structures