Geodesic
Yoneda theory for double categories
Theory and applications of categories, Tome 25 (2011), pp. 436-489 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18D05, 18A23, 18A25, 18A40, 18B15
Keywords: Double category, lax functor, module, modulation, representable, Yoneda lemma 
@article{TAC_2011_25_a16,
     author = {Robert Par\'e},
     title = {Yoneda theory for double categories},
     journal = {Theory and applications of categories},
     pages = {436--489},
     year = {2011},
     volume = {25},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a16/}
}
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Robert Paré. Yoneda theory for double categories. Theory and applications of categories, Tome 25 (2011), pp. 436-489. http://geodesic.mathdoc.fr/item/TAC_2011_25_a16/