Froehlich, Benedikt and Moser, Lyne (2024) YONEDA LEMMA AND REPRESENTATION THEOREM FOR DOUBLE CATEGORIES. THEORY AND APPLICATIONS OF CATEGORIES, 41. ISSN 1201-561X,
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We study (vertically) normal lax double functors valued in the weak double category C at 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Double categories; presheaves; Yoneda lemma; Grothendieck construction; representation theorem |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Jul 2025 10:29 |
| Last Modified: | 17 Jul 2025 10:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63695 |
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