Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Comments on Proposition 2.2.1.14

Go back to the page of Proposition 2.2.1.14.

Comment #335 by Claudius on

I don't know if it was intended or not, but here goes: The 2-morphisms in the diagram in the proof are denoted by simple arrows instead of the conventional double arrows.

Comment #387 by Kazuaki Miyatani on

In the proof, - I think each arrow in the diagram should be doubled (as in Comment #335). - In the top-right, should read . - Definition 2.1.1.5 should read Definition 2.2.1.1. - The commutativity of the quadrilaterals on the lower sides does not follow from Remark 2.2.1.13, but from the functoriality of associativity constraints.

Comment #388 by Kazuaki Miyatani on

(I am sorry that the appearance of my previous comment is broken... I don't see why; it works fine with the preview. Let me try again.)

In the proof, I think each arrow in the diagram should be doubled (as in Comment #335). In the top-right, should read . Definition 2.1.1.5 should read Definition 2.2.1.1. The commutativity of the quadrilaterals on the lower sides does not follow from Remark 2.2.1.13, but from the functoriality of associativity constraints.

Comment #389 by Kazuaki Miyatani on

Now it seems that the listing style in this comment does not work... Sorry for the difficulty to read.

Comment #390 by on

It seems like the preview and the website render Markdown a bit differently (which is to be expected, but it should be minimised), I will look into this, and sorry about the confusion it has caused!

Comment #1953 by Viktor Burghardt on

Typo: The top left corner has one parentheses too many. Cosmetic remark: For clarity and symmetry in the top right triangle could be under the arrow.

Comment #1960 by Kerodon on

Yep. Thanks!

There are also:

  • 4 comment(s) on Chapter 2: Examples of $\infty $-Categories
  • 2 comment(s) on Section 2.2: The Theory of $2$-Categories
  • 2 comment(s) on Subsection 2.2.1: $2$-Categories

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