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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 12th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a little bit of content to _[[cohomology operation]]_

   added a little bit of content to cohomology operation

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 26th 2016
   • (edited Apr 26th 2016)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThis would presumably be the entry to mention * Daniel Grady, Hisham Sati, _Primary operations in differential cohomology_, ([arXiv:1604.05988](https://arxiv.org/abs/1604.05988)) 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]]?

   This would presumably be the entry to mention

   • Daniel Grady, Hisham Sati, Primary operations in differential cohomology, (arXiv:1604.05988)

   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?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 7th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded bibliograpy details for * [[Daniel Grady]], [[Hisham Sati]], _Primary operations in differential cohomology_, Adv. Math. 335 (2018), 519-562 ([arXiv:1604.05988](https://arxiv.org/abs/1604.05988), [doi:10.1016/j.aim.2018.07.019](https://www.sciencedirect.com/science/article/pii/S0001870818302676?via%3Dihub)) <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/19">v19</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

   added bibliograpy details for

   • Daniel Grady, Hisham Sati, Primary operations in differential cohomology, Adv. Math. 335 (2018), 519-562 (arXiv:1604.05988, doi:10.1016/j.aim.2018.07.019)

   diff, v19, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2020
   • (edited Sep 2nd 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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](https://nforum.ncatlab.org/discussion/10105/bugs-and-feature-requests/?Focus=86583#Comment_86583)) <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/20">v20</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

   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)

   diff, v20, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2020
   • (edited Sep 2nd 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexTim, you just tried ([rev 21](https://ncatlab.org/nlab/revision/diff/cohomology+operation/21)) to hyperlink the intentionally misspelled name (as per [#4](https://nforum.ncatlab.org/discussion/3551/cohomology-operation/?Focus=86584#Comment_86584)). That doesn't make sense, does it? I have rolled back your edit. Let's wait until the bug gets fixed, and then add in the correct hyperlink.

   Tim, you just tried (rev 21) to hyperlink the intentionally misspelled name (as per #4).

   That doesn’t make sense, does it? I have rolled back your edit. Let’s wait until the bug gets fixed, and then add in the correct hyperlink.

6. • CommentRowNumber6.
   • CommentAuthorTim_Porter
   • CommentTimeSep 2nd 2020
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI 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.

   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.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[John Michael Boardman]], [[David Copeland Johnson]], [[W. Stephen Wilson]], _Unstable Operations in Generalized Cohomology_ ([pdf](https://hopf.math.purdue.edu/Boardman-Johnson-Wilson/bjw.pdf)), in: [[Ioan Mackenzie James]] (ed.) _[[Handbook of Algebraic Topology]]_ Oxford 1995 ([doi:10.1016/B978-0-444-81779-2.X5000-7](https://doi.org/10.1016/B978-0-444-81779-2.X5000-7)) <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/25">v25</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

   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)

   diff, v25, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2021
   • (edited Jan 19th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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](https://arxiv.org/abs/math/0605471), [euclid:agt/1513796856](https://projecteuclid.org/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](https://arxiv.org/abs/0711.3722), [euclid:hha/1251832594](https://projecteuclid.org/euclid.hha/1251832594)) * [[Tilman Bauer]], _Formal plethories_, Advances in Mathematics Volume 254, 20 March 2014, Pages 497-569 ([arXiv:1107.5745](https://arxiv.org/abs/1107.5745), [doi:10.1016/j.aim.2013.12.023](https://doi.org/10.1016/j.aim.2013.12.023)) * [[William Mycroft]], _Unstable Cohomology Operations: Computational Aspects of Plethories_, 2017 ([pdf](https://etheses.whiterose.ac.uk/20524/1/wm-thesis-final.pdf), [[MycroftUnstableCohomologyOperations.pdf:file]]) * [[William Mycroft]], [[Sarah Whitehouse]], _The plethory of operations in complex topological K-theory_ ([arXiv:2001.01608](https://arxiv.org/abs/2001.01608)) and tried to organize the list of references a little <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/26">v26</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

   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

   diff, v26, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJan 20th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added an Examples-section _[Cup-powers in multiplicative cohomology](https://ncatlab.org/nlab/show/cohomology+operation#CupPowersInMultiplicativeCohomology)_ 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](https://ncatlab.org/nlab/show/suspension%20spectrum#SmashMonoidalDiagonals). <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/27">v27</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

   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.

   diff, v27, current

10. • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 20th 2021
    • (edited Jan 20th 2021)
    • PermaLink
    Author: David_Corfield
    Format: MarkdownItexPresumably you don't want that first 'op' in $$ Ho \big( PointedTopologicalSpaces \big)^{op} \;\overset{ \;\; \;\; }{\hookrightarrow}\; Functors \Big( Ho \big( PointedTopologicalSpaces \big)^{op} , Set \Big) $$

    Presumably you don’t want that first ’op’ in

    $$Ho \big( PointedTopologicalSpaces \big)^{op} \;\overset{ \;\; \;\; }{\hookrightarrow}\; Functors \Big( Ho \big( PointedTopologicalSpaces \big)^{op} , Set \Big)$$
11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2021
    • PermaLink
    Author: Urs
    Format: MarkdownItexThanks! Fixed now. <a href="https://ncatlab.org/nlab/revision/diff/cohomology+operation/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/cohomology+operation/30">v30</a>, <a href="https://ncatlab.org/nlab/show/cohomology+operation">current</a>

    Thanks! Fixed now.

    diff, v30, current

12. • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 11th 2021
    • PermaLink
    Author: David_Corfield
    Format: MarkdownItexCame across this [MO answer](https://mathoverflow.net/a/385950/447) by Neil Strickland on Freyd's approach to higher cohomological operations. Anything useful to extract?

    Came across this MO answer by Neil Strickland on Freyd’s approach to higher cohomological operations. Anything useful to extract?