(Joint work with Prakash Panangaden and Rick Blute)
Segal's definition of a conformal field theory discusses "functors" for which the domain is not a category. There is an associative notion of composition or arrows, but there are no identities. Segal claim that this is not important, but we claim that one should not just freely add identities. Segal's original category can be seen as a nuclear ideal in a larger category and the functors one wants to consider as conformal field theories are nuclear functors. We will present one example of such a functor, due to Neretin.