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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI added to [[loop space]] a reference to Jim's classic article, which was only linked to from [[H-space]] and put pointers indicating that his delooping result in $Top$ is a special case of a general statement in any $\infty$-topos. By the way: it seems we have slight collision of terminology convention here: at "loop space" it says that H-spaces are homotopy associative, but at "H-space" only a homotopy-unital binary composition is required, no associativity. I think this is the standard use. I'd think we need to modify the wording at [[loop space]] a little.

   I added to loop space a reference to Jim’s classic article, which was only linked to from H-space and put pointers indicating that his delooping result in $Top$ is a special case of a general statement in any $\infty$-topos.

   By the way: it seems we have slight collision of terminology convention here: at “loop space” it says that H-spaces are homotopy associative, but at “H-space” only a homotopy-unital binary composition is required, no associativity. I think this is the standard use. I’d think we need to modify the wording at loop space a little.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 11th 2010
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   Author: zskoda
   Format: MarkdownItexI think the terminology at [[H-space]] is more sensitive and more conventional than the not that rare assumption that H-space is a H-monoid.

   I think the terminology at H-space is more sensitive and more conventional than the not that rare assumption that H-space is a H-monoid.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexSo what do you suggest we should do? We need to do something, it seems to me. Currrently the use of terminology at [[H-space]] and at [[loop space]] seems to be incompatible.

   So what do you suggest we should do? We need to do something, it seems to me. Currrently the use of terminology at H-space and at loop space seems to be incompatible.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeNov 11th 2010
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   Author: zskoda
   Format: MarkdownItexDo what you decide. I just said what is my impression of general conventions. I would not change [[H-space]] entry however.

   Do what you decide. I just said what is my impression of general conventions. I would not change H-space entry however.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have reworded at [[loop space]] as follows: > A loop space is an example of a [[A-∞ space]], in particular it is an [[H-space]]. Loop spaces admit this rich algebraic structure which arises from the fact that the based space $S^1$ carries a correspondingly rich co-algebraic structure, starting from the fact that the based space $S^1$ is an H-[[cogroup]].

   I have reworded at loop space as follows:

   A loop space is an example of a A-∞ space, in particular it is an H-space. Loop spaces admit this rich algebraic structure which arises from the fact that the based space $S^1$ carries a correspondingly rich co-algebraic structure, starting from the fact that the based space $S^1$ is an H-cogroup.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2010
   • (edited Nov 11th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI added the obligatory reference to May's book at [[loop space]]

   I added the obligatory reference to May’s book at loop space