15 May
1997
15 May
'97
8:12 a.m.
At the 64th PSSL at Braunschweig, I gave a talk about cartesian closedness of exact completions with an intention to cover equilogical spaces in the sense of Dana Scott (see D.S.Scott, A New category? Domains, Spaces and Equivalence Relations, preprint 1996). Unfortunately, Peter Johnstone found a flaw in my argument. I would like to announce the following result which covers equilogical spaces: Theorem: Let C be an infinitary extensive category. Then its exact completion ex(C) is cartesian closed iff C is weakly cartesian closed. Moreover, the embedding C-->ex(C) preserves exponentials.