TITLE: Where does Chu fit in with "Nice Categories of Spaces"?
QUESTION [7 upvotes]: Hi,
Here is a page about categories of spaces with "Nice" properties.  When we consider Chu spaces, I believe it was chosen to have certain properties that were "nice" at least to Pratt.  How does Chu fit in with the notion of "nice" that is outlined in the NLab site above?

REPLY [6 votes]: As one of the principal authors of the nLab page on "nice category of spaces" mentioned by the OP, let me quote: 

Within the nLab, “nice category of spaces” is a general but inexact term referring to nice or convenient properties one would like a category of spaces to have for some purpose (“space” here connoting something along topological lines)

I say this to correct the impression of Vaughan Pratt (seeing that he mentions my name in this regard, which was a surprise) that 'nice' in the nLab sense implies cartesian closure; for that, we use the more specific terminology "convenient category of topological spaces", after Ronnie Brown and Norman Steenrod who made that phrase famous. 'Nice' in the nLab sense is applied in a much more liberal and inclusive sense, as ought to be clear from the quote. Indeed, a number of examples given on the nLab page are not cartesian closed at all. (Many of the examples given however do emphasize various exactness properties.) 
Thus, there is no reason that categorical self-duality (or $\ast$-autonomous categorical structures) couldn't also be considered 'nice'. As the article says, 'nice' really only means nice for some purpose at hand. 
However, the main thrust of the nLab article is toward "spaces" in a topological sense. Chu spaces are, to my mind, "spaces" much more general than that. It's okay to call them "spaces" of course -- but consider that classical Chu spaces also include structures like $\mathbb{Z}_2$-vector spaces which would be a stretch to consider specifically topological. So Chu spaces go a bit beyond the types of structures originally envisioned for that article. Thus, the discrepancy isn't really centered on the word 'nice', but more on the word 'space'. 
If anyone wishes to discuss (or dispute!) the contents of an nLab article, the best and most proper place to do so would be on the nForum.