2020/09/11 by Tslil Clingman, Clingman, Tslil, Lyne Moser +1 · 1 citation
Mathematics · Medicine · #18A05 #18A25 #18A30 #18A40 #18N10 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Neuroblastoma Research and Treatments
paper · pdf · doi:10.48550/arxiv.2009.05545
openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a functor \mathcal V\colon DblCath,nps→ 2Cath,nps extracting from a double category a 2-category whose objects and morphisms are the vertical morphisms and squares. We give a characterisation of bi-representations of a normal pseudo-functor F\colon \mathbf Cop→ Cat in terms of double bi-initial objects in the double category 𝔼l(F) of elements of F, or equivalently as bi-initial objects of a special form in the 2-category \mathcal V𝔼l(F) of morphisms of F. Although not true in general, in the special case where the 2-category \mathbf C has tensors by the category 2=\0→ 1\ and F preserves those tensors, we show that a bi-representation of F is then precisely a bi-initial object in the 2-category El(F) of elements of F. We give applications of this theory to bi-adjunctions and weighted bi-limits.