Kerodon

Typo: in the last sentence of the proof of (a), $f_{0,\gamma}$, $f_{\beta,\gamma}$, and $f_{0,\beta}$ need to be replaced by $f_{\gamma,0}$, $f_{\gamma,\beta}$, and $f_{\beta,0}$, respectively.

Yep. Thanks!

Typo: Example 1.4.4.8 should read Exercise 1.4.4.8.

Yep. Thanks!

Type in the statement of $(b)$: by the collection of ...

Yep. Thanks!

I think in the proof of (b), if you want to write the coproduct as a transfinite composition, you have to change you $\tau \leq \sigma$ by $\tau\geq \sigma$'s and dually (and similarly with strict comparisons)

Otherwise your $j_\sigma$ goes from something indexed by $\sigma+1$ to something indexed by $\sigma$, and so that would be a dual transfinite induction and you need a co-well ordering on Q.

Yep. Thanks!