Katis, Piergiulio; Walters, Robert F. C. The compact closed bicategory of left adjoints. (English) Zbl 0980.18002 Math. Proc. Camb. Philos. Soc. 130, No. 1, 77-87 (2001). For each bicategory \({\mathcal B}\) there is a bicategory \(Sq{\mathcal B}\) of squares in \({\mathcal B}\): the objects are morphisms of \({\mathcal B}\) and the morphisms are squares in \({\mathcal B}\) containing a 2-cell. If \({\mathcal B}\) is monoidal then \(Sq{\mathcal B}\) becomes monoidal. The main result of the paper is that an object \(f\) in \(Sq{\mathcal B}\) has a right bidual if and only if \(f\) has a right adjoint and the domain and codomain of \(f\) have right duals. This implies that, if \({\mathcal B}\) is right autonomous (that is, admits all right duals), then the full sub-bicategory of \(Sq{\mathcal B}\) consisting of the left adjoint morphisms is also right autonomous. Reviewer: Ross H.Street (North Ryde) Cited in 2 Documents MSC: 18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) 18A10 Graphs, diagram schemes, precategories 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) Keywords:bicategory; autonomous; adjoint; bidual PDFBibTeX XMLCite \textit{P. Katis} and \textit{R. F. C. Walters}, Math. Proc. Camb. Philos. Soc. 130, No. 1, 77--87 (2001; Zbl 0980.18002) Full Text: DOI