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Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.

2 votes
Accepted

A fibration for the functor category functor

Section 7 of arxiv.org/pdf/2011.11042 discusses a general (op)lax twisted arrow category, which answers your question when applied to $Cat_{\infty}$. They cite arxiv.org/pdf/2009.11969 for introducing …
Victor Saunier's user avatar
4 votes

Is the unbounded derived $\infty$-category of a general abelian category stable?

If $A$ is small, it might be better to consider $D^b(A)$, the derived bounded category, which is also small. In this case, more is known: Corollary 7.4.12 of https://arxiv.org/pdf/1911.02338 proves th …
Victor Saunier's user avatar