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For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.

7 votes
0 answers
69 views

Colimits of underlying $n$-categories vs. $n$-uple categories

A double category is a category object in categories. There is a functor (of $1$-categories) $u : \mathrm{Cat}(1\mathrm{Cat}) \to 2\mathrm{Cat}$ from double categories to $2$-categories which is right …
3 votes
1 answer
140 views

Morphisms in category of left fibrations

I am trying to better understand the straightening-unstraightening equivalence of Lurie in the $\infty$-categorical setting. In the case that I am interested in, this equivalence states that $$ \mathr …