Comments 1 to 20 out of 2623 in reverse chronological order.
On
Weilong ZHAO
left
comment #2630
on
Exercise
4.8.4.4
in The Homotopy Theory of $\infty $-Categories
It seems that the order constructed here lacks reflexivity hence is not a partial order. Thus is not a -category (Proposition 057U).
On
Weilong ZHAO
left
comment #2629
on
Proposition
4.8.2.19
in The Homotopy Theory of $\infty $-Categories
Little typo: In (2) it seems that should be corrected as .
Moreover, in the proof of implication , in my understanding the right oblique map is bijective because of 052G. Maybe it's better to attach such a reference here and assume that our is -coskeletal as the reduction made at the first paragraph, so that 052G (2) can be applied directly.
On
Weilong ZHAO
left
comment #2628
on
Theorem
5.4.9.2
in Fibrations of $\infty $-Categories
Little typos: 1. In the webpage, the brackets in seem not to be depicted as expectation (at least for me).
2. In the diagram of (a), it seems that one shouldn't take core at the left corner.
3. "... is an -simplex of...", it seems that should be corrected as .
4. In the definition of , the target is a simplicial set hence it should be corrected as .
5. The enumerations , , in the definition of aren't compiled well on the webpage (at least for me).
Moreover, in (02S0) and in the definition of , is the abbreviation for intended or just a typo?
It seems that one can establish a stronger result: if is a Kan fibration of simplicial sets such that is surjective, then is a surjective simplicial map. In fact, for any vertex and vertex , if there exists an edge or in , one can lift it to an edge or in ; on the other hand, if and belong to the same component of , one can select a zig-zag diagram of edges in connecting them, which can be lifted inductively to a zig-zag diagram in connecting and a vertex of .
In the proof, "...we see that the degenerate -simplex coincides with on the horn ...", should be corrected as ? Otherwise we have directly without invoking the assumption is an -groupoid.
On
Weilong ZHAO
left
comment #2623
on
Example
9.1.1.7
in Large $\infty $-Categories
Little typo: A double "is" here.
On
Weilong ZHAO
left
comment #2622
on
Variant
5.5.5.9
in Fibrations of $\infty $-Categories
Here is the choice of terminology "-category of essentially -small -categories" intended or just a typo (with additional adjustive "essentially")?
On
Weilong ZHAO
left
comment #2621
on
Proposition
5.4.5.14
in Fibrations of $\infty $-Categories
Little typo: In the proof it seems that "" should be "", or "" by denoting .
On
Weilong ZHAO
left
comment #2620
on
Corollary
5.4.4.2
in Fibrations of $\infty $-Categories
Little typo: In the first sentence of the second paragraph of the proof, it seems that should be .
On
Weilong ZHAO
left
comment #2619
on
Proposition
5.4.3.8
in Fibrations of $\infty $-Categories
Little typo: it seems that in the expression of (c), should be .
On
Weilong ZHAO
left
comment #2618
on
Example
5.6.2.20
in Fibrations of $\infty $-Categories
Here it seems that to obtain one makes use of some functoriality of category of elements construction and sadly I failed to find a related discussion in the text. When we have a general natural transformation in , a possible way to introduce the associated simplicial map over is to apply Lemma 00B1 on and . However, since here is not assumed to be an -category, we lack the cocartesian hypothesis in Lemma 00B1 so that this kind of method doesn't work...
On Weilong ZHAO left comment #2630 on Exercise 4.8.4.4 in The Homotopy Theory of $\infty $-Categories
On Weilong ZHAO left comment #2629 on Proposition 4.8.2.19 in The Homotopy Theory of $\infty $-Categories
On Weilong ZHAO left comment #2628 on Theorem 5.4.9.2 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2627 on Proposition 3.5.4.18 in Kan Complexes
On Weilong ZHAO left comment #2626 on Proposition 3.5.6.12 in Kan Complexes
On Weilong ZHAO left comment #2625 on Remark 3.1.2.8 in Kan Complexes
On Weilong ZHAO left comment #2624 on Proposition 3.5.5.12 in Kan Complexes
On Weilong ZHAO left comment #2623 on Example 9.1.1.7 in Large $\infty $-Categories
On Weilong ZHAO left comment #2622 on Variant 5.5.5.9 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2621 on Proposition 5.4.5.14 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2620 on Corollary 5.4.4.2 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2619 on Proposition 5.4.3.8 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2618 on Example 5.6.2.20 in Fibrations of $\infty $-Categories
On Weilong ZHAO left comment #2617 on Example 7.3.9.5 in Limits and Colimits
On Weilong ZHAO left comment #2616 on Proposition 7.3.9.1 in Limits and Colimits
On Weilong ZHAO left comment #2615 on Proposition 7.3.8.23 in Limits and Colimits
On Kerodon left comment #2614 on Proposition 7.3.8.15 in Limits and Colimits
On Weilong ZHAO left comment #2613 on Proposition 7.3.8.15 in Limits and Colimits
On Kerodon left comment #2612 on Proposition 7.3.8.11 in Limits and Colimits
On Kerodon left comment #2611 on Proposition 7.3.8.8 in Limits and Colimits