Let P be a small category and A(B) a category such that the functor A → AP (B → BP) determined by the projection functor A x P → A (B x P → B) has an adjoint for all small category P. A functor G: B → AP has an adjoint functor if and only if it has and adjoint functor "via" evaluation. If Q is another small category and F: P → Q an arbitrary functor, the functor AF: AQ → AP has an adjoint functor.
@article{urn:eudml:doc:39769,
title = {Categor\'\i a exponencialmente fiel: Un teorema sobre functores adjuntos.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {39},
year = {1979},
pages = {267-275},
zbl = {0451.18002},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39769}
}
Martínez Calvo, Cristina. Categoría exponencialmente fiel: Un teorema sobre functores adjuntos.. Revista Matemática Hispanoamericana, Tome 39 (1979) pp. 267-275. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39769/