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/