Thanks to everyone who replied to my email. The consensus from people who claim to know (although there were some plausible guesses) is that the name is by analogy with "distributions" from functional analysis, which are "generalized functions." Thus changing "ion" to "or" we get that "distributors" are "generalized functors." On 11/16/05, Michael Shulman <shulman@math.uchicago.edu> wrote:

Hi,

Can anyone tell me the motivation for the use of the term "distributors" as a synonym for profunctors/bimodules? Is there something being distributed?

Thanks, Mike