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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 8th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Glen Bredon]], Section I.4 of: _[[Introduction to compact transformation groups]]_, Academic Press 1972 ([ISBN 9780080873596](https://www.elsevier.com/books/introduction-to-compact-transformation-groups/bredon/978-0-12-128850-1), [pdf](http://www.indiana.edu/~jfdavis/seminar/Bredon,Introduction_to_Compact_Transformation_Groups.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/coset/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/coset/21">v21</a>, <a href="https://ncatlab.org/nlab/show/coset">current</a>

   added pointer to:

   • Glen Bredon, Section I.4 of: Introduction to compact transformation groups, Academic Press 1972 (ISBN 9780080873596, pdf)

   diff, v21, current

2. • CommentRowNumber2.
   • CommentAuthortbraz
   • CommentTimeDec 13th 2023
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   Author: tbraz
   Format: TextI'm a little concerned the pasting law for homotopy pullbacks doesn't work in the way it's claimed in Remark 3.5. It seems to me that both the left square and total rectangle are homotopy pullbacks, which is insufficient to conclude the right square is a pullback. Am I missing something?

   I'm a little concerned the pasting law for homotopy pullbacks doesn't work in the way it's claimed in Remark 3.5. It seems to me that both the left square and total rectangle are homotopy pullbacks, which is insufficient to conclude the right square is a pullback. Am I missing something?
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 13th 2023
   • (edited Dec 13th 2023)
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   Author: Urs
   Format: MarkdownItexThanks for pointing this out. I have added ([here](https://ncatlab.org/nlab/show/coset#InGeometricHomotopyTheory)) a more precise pointer to the relevant [reverse pasting law for $\infty$-pullbacks](https://ncatlab.org/nlab/show/pasting+law+for+pullbacks#ReversePastingLawForInfinityGroupoids), which applies since the point inclusion into a delooping is an effective epi. On the other hand, we may understand the situation the other way around: First $G/H$ is defined by the second pullback, and then the ordinary $\infty$-pasting law gives the former one. Finally, I have added pointer to Ex 3.2.35 on [p. 104 here](https://arxiv.org/pdf/2112.13654.pdf#page=104) for more. <a href="https://ncatlab.org/nlab/revision/diff/coset/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/coset/24">v24</a>, <a href="https://ncatlab.org/nlab/show/coset">current</a>

   Thanks for pointing this out.

   I have added (here) a more precise pointer to the relevant reverse pasting law for $\infty$-pullbacks, which applies since the point inclusion into a delooping is an effective epi.

   On the other hand, we may understand the situation the other way around: First $G/H$ is defined by the second pullback, and then the ordinary $\infty$-pasting law gives the former one.

   Finally, I have added pointer to Ex 3.2.35 on p. 104 here for more.

   diff, v24, current