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arXiv · 2004.01313

2-limits and 2-terminal objects are too different

tslil clingman·Lyne Moser
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Abstract

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 2-limits and 2-terminal objects in the various choices of slice 2-categories of 2-cones are false. Furthermore we show that, even when weakening the 2-cones to pseudo- or lax-natural transformations, or considering bi-type limits and bi-terminal objects, there is still no such correspondence.

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tslil clingman, Lyne Moser. 2020-04-03. 2-limits and 2-terminal objects are too different. https://arxiv.org/abs/2004.01313

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