There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, which we then apply to internal categories. Finally, we describe a doctrinal setting.
Keywords: adjoint functor; enriched category; bicategory; Kleisli cocompletion
2010 MSC: 18A40; 18D10; 18D05
Theory and Applications of Categories, Vol. 27, 2012, No. 4, pp 47-64.
Published 2012-06-12.
http://www.tac.mta.ca/tac/volumes/27/4/27-04.dvi
http://www.tac.mta.ca/tac/volumes/27/4/27-04.ps
http://www.tac.mta.ca/tac/volumes/27/4/27-04.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/27/4/27-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/27/4/27-04.ps