Chu Spaces

Another name in the name index I worked on was "Chu". It was related to "Chu spaces". The article "Chu space" in Wikipedia says:

The Chu space concept originated with Michael Barr and the details were developed by his student Po-Hsiang Chu, whose master's thesis formed the appendix of the book M. Barr, *-Autonomous categories, Springer-Verlag Lecture Notes in Mathematics 752, 1979.

The relation between the author of this concept and the concept's name is very interesting.

M. Barr, in his article "The Chu construction: History of an idea", Theory and Applications of Categories, 17:1, 10-16 (2006), writes:

<...>
It seemed clear that this gave *-autonomous category, but there were a number of unpleasant details to be verified. Since my student, Po-Hsaing Chu needed a master's project, so I asked him to verify them, which he did in [Constructing *-autonomous categories, M.Sc. thesis, McGill university, 1978] [APPENDIX to M. Barr, *-Autonomous categories]"

I now had expanded from six to infinity the repertory of known *-autonomous categories. At this point, the construction, and in fact the whole idea of *-autonomous categories was more-or-less forgotten, not least by me.

In the earlier paper M. Barr [The Chu construction, Theory and Applications of Categories, 2:2, 17-35 (1996)] gave the history of Chu construction (Section 6 "The true history of Chu categories").

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So I wrote down the obvious definitions of morphism. It then occurred to me wonder if the resultant category was closed or monoidal and quickly discovered that it was both, modulo the checking of a morass details. Since Chu needed a topic for his master's degree, I set him this task and the appendix to [Barr, 1979] was the result. But the story does not end there. Or rather, it would have ended there since neither I nor anyone else found any interest in this rather formal construction. But the year 1987 saw a renewed interest in *-autonomous categories as models of Girard's linear logic and then Vaughan Pratt and his student Vineet Gupta rediscovered the Chu construction and begun to study it in earnest.
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Probably the main conclusion to draw from this history is that, as with most mathematical discoveries, it is a mistake to attribute it to any one person. It was born out of need, with a number of midwives, but no real discoverer.

The APPENDIX to the monograph [Barr, 1979] (of some thirty pages) seems to be the only publication by Chu on "Chu spaces".
So, the Chu spaces are named after Po-Hsaing Chu.


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Joe Dolan (born Joseph Francis Robert Dolan, 16 October, 1943 in Mullingar, County Westmeath, Ireland) is a singer of easy listening songs.