Exponentiable functors between quantaloid-enriched categories

Maria Manuel Clementino , Dirk Hofmann , Isar Stubbe (1, 2)

1 ULCO - Université du Littoral Côte d'Opale
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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 [1980] and Dyckhoff and Tholen [1987].

Domaines: Mathématiques [math]; Informatique [cs]; Physique [physics]

Maria Manuel Clementino, Dirk Hofmann, Isar Stubbe. Exponentiable functors between quantaloid-enriched categories. Applied Categorical Structures, 2009, 17 (1), pp.91-101. ⟨10.1007/s10485-007-9104-5⟩. ⟨hal-03606837⟩