تقرير
Yoneda lemma and representation theorem for double categories
| العنوان: | Yoneda lemma and representation theorem for double categories |
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| المؤلفون: | Fröhlich, Benedikt, Moser, Lyne |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, 18N10, 18D30, 18D60, 18D40 |
| الوصف: | We study (vertically) normal lax double functors valued in the weak double category $\mathbb{C}\mathrm{at}$ 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 $\mathrm{Cat}$ 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. Comment: 57 pages; comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.10640 |
| رقم الأكسشن: | edsarx.2402.10640 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |