Representables for double categories are defined to be lax morphisms into a certain double category of sets. We show that horizontal transformations from representables into lax morphisms correspond to elements of that lax morphism. Vertical arrows give rise to modules between representables. We establish that the Yoneda embedding is a strong morphism of lax double categories which is horizontally full and faithful and dense.
Keywords: Double category, lax functor, module, modulation, representable, Yoneda lemma
2000 MSC: 18D05, 18A23, 18A25, 18A40, 18B15
Theory and Applications of Categories, Vol. 25, 2011, No. 17, pp 436-489.
Published 2011-11-17.
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