added publication data to this item:

- Kuen-Bang Hou (Favonia), Eric Finster, Dan Licata, Peter LeFanu Lumsdaine,
*A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory*, LICS ’16 (2016) 565–574 [arXiv.1605.03227, doi:10.1145/2933575.2934545]

i have added publication data to the item

- Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal,
*A Generalized Blakers-Massey Theorem*, Journal of Topology**13**4 (2020) 1521-1553 $[$arXiv:1703.09050, doi:10.1112/topo.12163$]$

and added the comment that this is

]]>generalizing to the case where the (n-connected, n-truncated) factorization system may be replaced by more general modalities

added pointer to:

- Tammo tom Dieck, Klaus Heiner Kamps, Dieter Puppe, Section 15 of:
*Homotopietheorie*, Lecture Notes in Mathematics**157**Springer 1970 (doi:10.1007/BFb0059721)

Yesterday I pasted it into our Sandbox, and it came out not looking well. Maybe better if we could have the source rendered by some software that does it decently (maybe just the GitHub output, or maybe there is something better) and then store this output in a pdf or the like.

]]>You’re welcome :-)

The urls are not proper markdown links (GH just links them automatically), and I think the names could be bumped down a notch in heading size, but I don’t mind if it’s put on the HoTT web as a page.

]]>Thanks very much by the way!

]]>Or even better, since the format is markdown, it could be just pasted into an nLab page rather than attached as a file. If we don’t think it’s appropriate as a standalone nLab page for some reason, we could put it on the HoTT web instead.

]]>It can be renamed to a .txt if you want. The .md just makes GitHub render it with some minimal formatting, making links active etc.

]]>I have replaced the link to G+ with the link to David R.’s GitHub page (here)

I would like to have this downloaded as a file to the $n$Lab, but I don’t know how to convert that md-format to anything.

]]>The file? I don’t mind.

]]>Well done! Should we upload it to the nLab?

]]>I’m extracting the post and comments and will place it in on my GitHub Sandbox so that we have a record of it.

**Edit**: see here

Can we copy it out of the Wayback machine into a page here?

]]>The discussion is still in the source of the Wayback Machine page that David Corfield linked to, it’s just not being displayed when the page is rendered by our browsers. Someone who knows more HTML than I do could alter the source to make it display correctly or clear it up so it can be read directly.

]]>Oops, no, I didn’t export it. Figured there was nothing there necessary to keep for posterity, but of course there was: this memorable exchange between Favonia and Charles Rezk. Sorry, that’s a real loss.

]]>Re 16: Urs, did you export your G+ content before it got deleted?

Re 17: Urgh, I forget – sometimes there is an off-by-one shift in the indexing. I know there is an off-by-one shift between what a classical homotopy theorist calls an $n$-connected map (or more often an $n$-equivalence) and what HoTT people call an $n$-connected map, because ours is based on the connectivity of the fiber and theirs on the connectivity of the cofiber. I forget what the indexing is for “connective”; maybe it matches the HoTT indexing and a different word was chosen to avoid conflict with the classical terminology?

]]>two maps out of the same domain which are $n_1$-connective and $n_2$-connective

Is ’connective’ preferred to ’connected’ in this context, or just used as a synonym?

]]>The page points to a g+ discussion which of course is no longer supported. The wayback machine gives me a glimpse of the old page but then disappears. Do we have a way to retrieve it?

]]>The HoTT-proof is finally out: FFLL 16.

]]>Zoran, what sort of result do you think might hold in strong shape? and how general a strong shape conetxt are you thinking of?

]]>I have indented the paragraph with abstract for Lumsdaine’s annoucement talk. I have added the reference for the Blakers-Massey in shape theory. It seems that the case of strong shape theory is still open (I have some interest in working on that case).

]]>I have added a brief remark here that there is a tower of higher cubical generalization of the Blakers-Massey theorem, which jointly say equivalently that the identity functor on $\infty Grpd$ is Goodwillie-analytic.

]]>Does Chachólski’s argument actually prove the full strength of the Blakers–Massey Theorem? If I read Theorem 1.B of *A generalization of the triad theorem of Blakers-Massey* correctly, it only implies that given a homotopy pushout

with $A \to B$ $p$-connected and $C \to D$ $q$-connected (in the HoTT convention), the suspension of $A \to B \times_D^{\mathrm{h}} C$ is $(p+q+1)$-connected. That seems strictly weaker than saying that $A \to B \times_D^{\mathrm{h}} C$ itself is $(p+q)$-connected (there are non-contractible spaces with contractible suspensions).

]]>Yes, that’s what I say; and that it is the first one I know in the literature.

]]>