partial adjoints

Hello all, Sender: categories@mta.ca Precedence: bulk Reply-To: Peter Bubenik <peter.bubenik@gmail.com> Has anyone studied pairs of functors for which there exists a unit, but not a counit? Is there a name for such things? In the case of interest, the functors are between Cat and Met, the category of (extended pseudo-) metric spaces and 1-Lipschitz maps. The unit provides a characterization of certain coherent maps of metric spaces. Further details may be found in https://arxiv.org/abs/1603.07406. Thanks, Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]