I will be here at Oxford until 30 May. Oege de Moor, in the Computing Laboratory here, would like to know if every endofunctor on the category of sets preserves weak pullbacks. Any information on this would be appreciated. More generally, he is interested in lifting functors to the category of relations. Both he and I would like to know of papers written on this subject. --Charles Wells Subject Re: new address etc
I replied much too quickly to the Charles Wells question. What is correct is that any functor that preserves all finite weak limits preserves all finite limits. For an example of an endofunctor on SETS that fails to preserve weak pullbacks consider the functor that takes the empty set to the empty set and everything else to a one-element set. For a counterexample to my hasty response consider the covariant power- set functor (using direct images); it preserves weak pullbacks but not pullbacks. Peter Freyd
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Charles.Wells＠PRG.OXFORD.AC.UK -
pjf＠linc.cis.upenn.edu