# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

## Comments on Proposition 2.4.6.8

Go back to the page of Proposition 2.4.6.8.

Comment #405 by Nicholas Mertes on

Can we state a similar proposition in the "other direction?" In particular, let $C$ be an $\infty$-category. Can we endow $hC$ with the structure of a locally Kan simplicial category such that the $\infty$-category $N^{hc}(hC)$ is isomorphic (or perhaps only equivalent) to $C$? This would mean that we could use a simplicial structure on $hC$ to "put back" the information lost by passing from $C$ to $hC$.

Comment #406 by Kerodon on

The projection map from an $\infty$-category to its homotopy category usually does not have a section.

There are also:

• 2 comment(s) on Chapter 2: Examples of $\infty$-Categories
• 2 comment(s) on Section 2.4: Simplicial Categories

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