Geodesic
Yoneda lemma and representation theorem for double categories
Theory and applications of categories, Tome 41 (2024), pp. 1698-1782.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We study (vertically) normal lax double functors valued in the weak double category Cat of small categories, functors, profunctors and natural transformations, which we refer to as lax double presheaves. We show that for the theory of double categories they play a similar role as 2-functors valued in Cat for 2-categories. We first introduce representable lax double presheaves and establish a Yoneda lemma. Then we build a Grothendieck construction which gives a 2-equivalence between lax double presheaves and discrete double fibrations over a fixed double category. Finally, we prove a representation theorem showing that a lax double presheaf is represented by an object if and only if its Grothendieck construction has a double terminal object.
Publié le :
Classification : 18N10, 18D30, 18D60, 18D40
Keywords: Double categories, presheaves, Yoneda lemma, Grothendieck construction, representation theorem 
@article{TAC_2024_41_a48,
     author = {Benedikt Fr\"ohlich and Lyne Moser},
     title = {Yoneda lemma and representation theorem for double categories},
     journal = {Theory and applications of categories},
     pages = {1698--1782},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a48/}
}
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Benedikt Fröhlich; Lyne Moser. Yoneda lemma and representation theorem for double categories. Theory and applications of categories, Tome 41 (2024), pp. 1698-1782. http://geodesic.mathdoc.fr/item/TAC_2024_41_a48/