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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.
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.
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.
Do what you decide. I just said what is my impression of general conventions. I would not change H-space entry however.
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.
I added the obligatory reference to May’s book at loop space
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