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added a little bit of content to cohomology operation
This would presumably be the entry to mention
where the differential cohomology diagram and cohesion are to be found on p.9.
What does the ’primary’ part mean? WHat’s the relationship to primary homotopy operation?
added bibliograpy details for
I have touched the references, added some publication data, some brief comment on content, and rearranged a little for a more systematic list.
Intentionally misspelled (and un-linked) Martin Tangora’s name, because otherwise the entry wouldn’t save, due to an overreactive spam detector (see here)
I was trying to understand what on earth was happening. It is quite mystifying why ’tango’ should be considered spam!!! As you said, we should wait until that bug is fixed.
added pointer to:
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
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.
Presumably you don’t want that first ’op’ in
$Ho \big( PointedTopologicalSpaces \big)^{op} \;\overset{ \;\; \;\; }{\hookrightarrow}\; Functors \Big( Ho \big( PointedTopologicalSpaces \big)^{op} , Set \Big)$Came across this MO answer by Neil Strickland on Freyd’s approach to higher cohomological operations. Anything useful to extract?
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