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I added a bunch of entries to homotopy - contents – mostly all the variants of homotopy groups – and inserted the floating TOC to all pages listed there
One result of that list is that the actual theory of homotopy seems to divided into three parts, none of which actually handles the central case, i.e. homotopy theory per se!. Although this is fine and not at all serious, it might look a bit odd to a ’visitor’ and I am not sure how to fix the oddness. We could have the main homotopy theory page saying something motivational, with the current homotopy theory page being renamed to ’Standard homotopy theory and the n-POV’ and direct the browsing reader to standard texts such as Hatcher for their introduction to homotopy theory as such in the outside /entry level page. As this would mean a structural change, we should probably discuss it briefly, before doing anything (or nothing) but in any case it is not a serious oddness, so can be left ’as is’.
I agree, at list a link to algebraic topology should be included but it is not clear where.
make a suggestion for how to reorganize things.
I put in a couple of headers to fix the impression that homotopy theory is divided into three parts and to find a place for algebraic topology. This probably doesn’t fix everything, however!
4: As I stated in 3, it is not clear to me where to include it, so I can not suggest where (the organization over there is rather different than the way I understand/classify the things.), but rather only that I feel it should be somewhere there.
As homotopy theory was originally part of algebraic topology, perhaps the answer is already at hand. The Alg. Top. entry looks quite good. (Perhaps leave it as it is.) The next problem is that homotopy theory only really considers the models category nPOV approaches, which is fine until one tries to link to the more classical treatment of homotopy theory, and even algebraic homotopy theory does not fit into the current framework. We may need another entry with a historical or classical over view of homotopy theory. I do not really like restricting homotopy theory to be just the QMC stuff as there is a lot more to it than that, but that is the name of the page and I do not fancy looking through the rest of the Lab to change all the links. A possible disambiguation would be to add something like ‘This page discusses the Theory of Homotopy Theories, as derived from the homotopical algebra approach to the subject. For other topics within the general area of Homotopy Theory look at the list of related entries.’ I will copy that over and see how it looks to you all.
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