Re: thoughts arising from a letter of Lawvere

[Max Kelly <maxk@maths.usyd.edu.au>]

Martin Escardo (Categories 8 Jan.) is correct in surmising that the
results of Brian Day's 1968 M.Sc. thesis are included, in a much more
general form, as an example in his 1972 article in JPAA. My point was only
the history of the matter; the 1972 paper is one of three which together
expound the content of Brian's Ph.D. thesis, and appeared four years later
than his Masters degree. In the interim the adjunction between topological
spaces and Spanier's quasi-spaces, and the relation of this to
compactly-generated spaces, had been observed and published by two or
three other of our colleagues; Booth was one, and there was at least one
more whose name escapes me. Brian was then rueful about not submitting the
M.Sc. thesis for publication in 1968; as his supervisor, I shared his rue.

Martin also seeks more information about the hidden category theory
behind my 1970 paper with Brian. There was never anything like a
"categorical version" that got turned into a "topological" one;
we translated as we went. I believe my 2 Jan. letter to Categories
contains enough hints to make a reconstruction straightforward, even if
a bit long and tedious.

Max Kelly.