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Stream: deprecated: translation

Topic: Bikategorien af Profunktorer

Nathanael Arkor (Oct 27 2021 at 12:27):

The thesis I'm interested in is Justesen's Bikategorien af Profunktorer. In particular, the thesis is cited by Johnstone and Wraith as being a (the first?) reference that monads in Prof are bijective-on-objects functors. I'd like to know if this citation is correct, and what the precise reference is (e.g. the proposition or page number). I think pages 36 – 39 (of the PDF) or anywhere in §6 are the most likely candidates because I see the term "promonad" there. I'm interested to know more generally what kind of results are proven in §6. That's quite a wide range, but hopefully(!) most of the pages are proofs, so can be skipped over.

Robin Kaarsgaard (Oct 27 2021 at 14:08):

I believe that the theorem you are after is the following (p. 81, "Struktursætning for promonader"):

"Structure theorem for promonads: There is a one-to-one correspondence between isomorphism classes of promonads on $\mathbb{A}$ and equivalence classes of functors $\psi$ from $\mathbb{A}$ to small categories with the same set of objects as $\mathbb{A}$, such that $\psi$ is identity on objects."

Nathanael Arkor (Oct 27 2021 at 14:29):

Perfect, thank you very much!