The core of adjoint functors

Ross Street

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.

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