# 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

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2-limits and 2-terminal objects are too different

- Mathematics
- 2020

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 relating… Expand

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