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    $\begingroup$ See en.wikipedia.org/wiki/Lusternik%E2%80%93Schnirelmann_category for the definition. I suppose Jeff uses the convention of deleting one from the Wikipedia definition (also mentioned there) so that cat (sphere)=1. $\endgroup$ Commented Jan 21, 2017 at 18:33
  • $\begingroup$ Just a stupid question - what is the cup length of $SP(n)$? $\endgroup$ Commented Mar 14, 2017 at 9:29
  • $\begingroup$ The cohomology is an exterior algebra on $n$ generators, so the cup length is $n$. $\endgroup$ Commented Mar 14, 2017 at 14:31
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    $\begingroup$ @JeffStrom, I would suggest evaluating the systolic category of $Sp(n)$ first. This is often easier to compute, and the two categories are equal in many cases. $\endgroup$ Commented Mar 15, 2017 at 13:14