Kerodon

I believe there is a typo in the first diagram on this page; one of the objects $C$ should be a $D$.

There is the same typo as Daniel points out (a $C$ that should be a $D$) in Proposition 0040 as well.

Ah, good catch. Thanks!

[Typo] "Example 1.3.3.3. ... Then $f$ and $g$ are homotopic as morphisms of the $\infty$--category $\operatorname{Sing}_{\cdot}(\mathcal{C})$ (in the sense of Definition 1.3.3.1) if and only if the paths ..."

[Typo] "Proposition 1.3.3.6. ... (2) ..., and $d_2(\tau) = \operatorname{id}_C$, as depicted in the diagram ..."

[Typo] Proof of Proposition 1.3.3.6: The $X$s and $Y$s should be $C$s and $D$s.

Yep. Or better, the C's and D's should be X's and Y's... Thanks!

"Then the tuple $( \sigma _0, \bullet , \sigma _2, \sigma _3)$ determines a map of simplicial sets $\tau _0: \Lambda ^3_1 \rightarrow \operatorname{\mathcal{C}}$ (see Exercise 1.1.2.14)"
I don't think this exercise is quite what we want. The exercise states that the image of the $(f : \Lambda^n_i \rightarrow S_\bullet) \mapsto ( f\circ\delta^{j} ) _{j\in[n]\setminus \{ i\}}$ is injective and consists of "incomplete" sequences satisfying some property. But here, it appears that we're going the other way i.e., we find a incomplete sequence $( \sigma _0, \bullet , \sigma _2, \sigma _3)$ satisfying some properties, and then the exercise gives us the map $\tau _0$. So, I think the exercise should be rephrased slightly to say the image of $(f : \Lambda^n_i \rightarrow S_\bullet) \mapsto ( f\circ\delta^{j} ) _{j\in[n]\setminus \{ i\}}$ consists of all "incomplete" sequences satisfying some property (or we could say the map is bijective) to properly apply Exercise 1.1.2.14.