In his PhD thesis, Categorical Structure of Continuation Passing Style, Thielecke studies the ⊗¬-categories, which are premonoidal categories with structure (namely, a functor ¬ which is adjoint to itself), in order to model the semantics of continuation-passing style languages.

I've been studying his work for some time now, but I'm not really familiar to literature about category theory. So my question is, and it might sound silly: how should I pronounce "⊗¬-category"? In fact, I could rephrase this: if I were to write about those categories in a paper, how should I refer to them? Should one write it in full, or simply just refer to them as ⊗¬-categories all the time and leave the pronunciation as an open problem?

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    $\begingroup$ A version of this problem was solved by Victor Borge. youtube.com/watch?v=Qf_TDuhk3No $\endgroup$ Jun 17, 2020 at 4:03
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    $\begingroup$ @AndreasBlass, I would like to write a comment but, I cannot stop laughing... $\endgroup$ Jun 17, 2020 at 4:48
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    $\begingroup$ If you're planning to write a paper, there's no advantage in trying to write out the pronunciation: you may just use the symbols. If I was trying to pronounce the name, I would say "tensor-not category" or similar, analogously to "dagger category" for †-category or "star algebra" for *-algebra. $\endgroup$
    – varkor
    Jun 17, 2020 at 10:44
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    $\begingroup$ @varkor I actually find it incredibly distracting to have symbols that I cannot pronounce in my head while reading… $\endgroup$ Jun 17, 2020 at 11:44
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    $\begingroup$ How about "TN-category" (for "tensor-negation")? $\endgroup$ Dec 22, 2020 at 19:20

1 Answer 1


I shared an office with Hayo Thielecke in the late 1990s.

The pronunciation he used was "Tensor-NOT-category".

  • $\begingroup$ I'm still working on my paper on the formalization of the CPS-calculus, I'll take note of that. Thank you very much! $\endgroup$ Aug 20, 2021 at 0:56

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