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added a new Examples-section Integral versus real cohomology to fiber sequence
(and renamed the original fibration sequence and made it a redirect to that – but the cache bug is in the way,as usual).
added a detailed proof of how homotopy fibers of oo-functor categories are computed in terms of over-categories.
if you think about it, the proof I just mentioned is the full-fledged version of the proof that we sketched previously in the section In terms of sections at twisted cohomology. I have added some more sentences to this effect now.
added an Examples section on how equivalences are characterized by having contractible homotopy fibers
The last reference in the fiber sequence entry has now been published. I have updated the entry. The previous title at this point was wrong by the way. It did not correspond to the paper to which the link refered. I hope this is now correct.
An Anonymous has made changes to fiber sequence in the section on Mayer-Vietoris. I do not understand their point. They did change something to $A\times C$, but from the pullback this should be $A\times B$ and … in other words the entry seems to be a mess at this point (glancing at it). The diagram is wrong as well. There are several ways to fix it, but I am not sure which is intended.
Thanks for the alert. I have fixed it now (here), both the original diagram as well as the fiber sequence afterwards, exchanging Bs for Cs.
I suppose somebody saw the typo, kindly went to fix it, but then didn’t exactly.
That is what I suspected.
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