added pdf-link for

- John Michael Boardman,
*Stable Operations in Generalized Cohomology*(pdf)

I have added an Examples-section *Cup-powers in multiplicative cohomology* with details of how $\alpha \mapsto \alpha \cup \alpha$ is an (unstable) cohomology operation on any multiplicative cohomology theory; amplifying how, via the Yoneda lemma on the homotopy category, this comes down to there being smash-monoidal diagonals on suspension spectra.

Even without the error message, the diff on my revision 7 is not very useful, as it fails to render all the LaTeX-style code. My understanding is that this is because the renovated parser operates only on the public page, but nor on diff-s nor on the page history.

For that reason I try to keep pointing directly to where I made changes. In the present case, the changes are the entirety of this section.

]]>trying to see the diff of monoidal category with diagonals gave me

500 Internal Server Error

several times repeatedly. But while I was trying to track the error down and report it it went away.

]]>Thanks for looking into this!

]]>I have tried to turn the line on connective covers of ring spectra into something more informative. Now it reads:

The connective cover construction extends from plain spectra to E-∞ ring spectra (May 77, Prop. VII 4.3) …

(Or so it says in Baker-Richter 05, p. 1. It takes much chasing of notation to deduce what May 77, Prop. VII 4.3 really says, I haven’t really checked.)

…though besides the canonically inherited ring structure the connective cover may sometimes carry other ring structures (Baker-Richter 05, p. 1).

Then there was a pointer to Lurie, prop. 7.1.3.13 but in checking again, the numbering seems to have changed and I haven’t tracked down the relevant passage yet.

Ignorant question:

How about just homotopy-commutative ring spectra? Does the connective cover construction extend to these functorially?

]]>Re #1: The journal in which this article was published is being scanned and uploaded here: http://www.mathnet.ru/php/archive.phtml?jrnid=dan&wshow=contents&option_lang=eng

So far they have volumes up to 1957, whereas Postnikov’s 4-page note was published earlier, in 1951.

]]>I have expanded out (here) the example of the smash product on pointed sets/spaces. Since the same example also serves in related entries, I have written it into its own entry *smash-monoidal diagonals – section* and `!include`

ed it here

a bare sub-section, meant to be `!include`

-ed into the Examples-sections of relevant entries, such as at *monoidal category with diagonals*, *smash product* and *cup product*

fixed notation in the second formula in the proof of this Prop.:

(The adjoined base point $(-)_+$ to the symmetric group factor was previously displayed below the formula beneath the underbrace below the symmetric group symbol that it really belonged to. And in the second line of that formula under the brace, the corresponding $(-)_+$ had been missing.)

]]>coming here to add “selected writings”, I have adjusted/updated the wording a little

]]>Changed the section number of the HoTT book reference to 7.3 on truncations:

Is there another HoTT reference to mention with a more extensive treatment? Something also to add at Postnikov tower in an (infinity,1)-category.

]]>brief `category:people`

-entry for hyperlinking references at *cohomology opperation*

added more references:

Andrew Stacey, Sarah Whitehouse,

*Stable and unstable operations in mod $p$ cohomology theories*, Algebr. Geom. Topol. Volume 8, Number 2 (2008), 1059-1091 (arXiv:math/0605471, euclid:agt/1513796856)Andrew Stacey, Sarah Whitehouse,

*The Hunting of the Hopf Ring*, Homology Homotopy Appl. Volume 11, Number 2 (2009), 75-132. (arXiv:0711.3722, euclid:hha/1251832594)Tilman Bauer,

*Formal plethories*, Advances in Mathematics Volume 254, 20 March 2014, Pages 497-569 (arXiv:1107.5745, doi:10.1016/j.aim.2013.12.023)William Mycroft,

*Unstable Cohomology Operations: Computational Aspects of Plethories*, 2017 (pdf, MycroftUnstableCohomologyOperations.pdf:file)William Mycroft, Sarah Whitehouse,

*The plethory of operations in complex topological K-theory*(arXiv:2001.01608)

and tried to organize the list of references a little

]]>Clean up reference to Richard W’s thesis (he’s not in math genealogy, so I don’t know the actual year of it, only the arXiv submission year)

]]>added pointer to

- John Michael Boardman, David Copeland Johnson, W. Stephen Wilson,
*Unstable Operations in Generalized Cohomology*(pdf), in: Ioan Mackenzie James (ed.)*Handbook of Algebraic Topology*Oxford 1995 (doi:10.1016/B978-0-444-81779-2.X5000-7)

(since unstable operations on stable cohomology is really operations on their image in non-abelian cohomology)

]]>brief `category:people`

-entry for hyperlinking references at *Johnson-Wilson spectrum*, *cohomology operation* and elsewhere

added full author list and pdf-link for

- John Michael Boardman, David Copeland Johnson, W. Stephen Wilson,
*Unstable Operations in Generalized Cohomology*(pdf), in: Ioan Mackenzie James (ed.)*Handbook of Algebraic Topology*Oxford 1995 (doi:10.1016/B978-0-444-81779-2.X5000-7)

added pointer to:

- John Michael Boardman, David Copeland Johnson, W. Stephen Wilson,
*Unstable Operations in Generalized Cohomology*(pdf), in: Ioan Mackenzie James (ed.)*Handbook of Algebraic Topology*Oxford 1995 (doi:10.1016/B978-0-444-81779-2.X5000-7)

added pointer to

- W. Stephen Wilson,
*Hopf rings in algebraic topology*, Expositiones Mathematicae, 18:369–388, 2000 (pdf)

(this used to be referenced only at *W. S. Wilson* and without the pdf link, so I completed the item and copied it to here)

have expanded the list of “Selected writings”: more entries, more complete bib-info

]]>I have touched the list of QED/QCD bound states, slight expanding, slightly re-organizing

]]>a brief stub, to make links work

]]>Searching for Hoyer’s webpage, it’s curious to note that on the top of the page, under “current research”, there is a single link, and it goes to a single-page note “Remarks on bound states in perturbation theory”, dated from four days ago, with a list of nine brief statements/questions (pdf). I wonder how that came about.

]]>