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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2010

    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 TopTop 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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 11th 2010

    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.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2010

    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.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 11th 2010

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

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2010

    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 1S^1 carries a correspondingly rich co-algebraic structure, starting from the fact that the based space S 1S^1 is an H-cogroup.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2010
    • (edited Nov 11th 2010)

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