Corpus ID: 221640897

Bi-initial objects and bi-representations are not so different

@article{Clingman2020BiinitialOA,
  title={Bi-initial objects and bi-representations are not so different},
  author={T. Clingman and Lyne Moser},
  journal={arXiv: Category Theory},
  year={2020}
}
We introduce a functor $\mathcal V\colon\textsf{DblCat}_{\mathrm{h,nps}}\to \textsf{2Cat}_{\mathrm{h,nps}}$ 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 $F\colon \mathbf C^{\operatorname{op}}\to \textsf{Cat}$ in terms of double bi-initial objects in the double category $\mathbb{E}\operatorname{l}(F)$ of elements of $F$, or equivalently as bi-initial… Expand
2-limits and 2-terminal objects are too different
In ordinary category theory, limits are known to be equivalent to terminal objects in the slice category of cones. In this paper, we prove that the 2-categorical analogues of this theorem relatingExpand

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