8 Sep
1998
8 Sep
'98
5:58 p.m.
Has anybody seen the following symmetric closed monoidal category? Let #A# be a category tripleable over Set. Let #V# be the comma category (F,#V#), F being the free functor. So an object (S,s,A) is an arrow s:FS --> A and a map (S,s,A) to (T,t,B) is a pair f: S --> T and g: A --> B making the obvious square commute. The closed structure (S,s,A) --o (T,t,B) is a certain arrow of the form (Hom((S,s,A),(T,t,B),?,B^S). The monoidal structure is fairly ugly, but it exists. Of course, an object (S,s,A) can also be thought of as an S-tuple of elements of A, by adjointness. Michael