I have two questions, which I hope, someone has the answer or a pointer where I could obtain some hints: Question 1: Let C be a CCC, which not necessarily is a free CCC. Is there a reasonable way of typing C ? More precisely: If X is an object in a (not necessarily free) Cartesian closed category, is it possible to tell, whether X is of the form Y => Z or of the form Y x Z, with suitably chosen Y and Z ? The problem I have is the following: Assume D is a free CCC constructed over a set of constants. Now identify some of the objects in D to yield the not-free CCC C. Now we could think of a situation, where an object in C is of the form U x V and at the same time of the form W => R. On the other hand, the restrictions on the identifications of D-objects, which come from the requirement, that C again is a CCC, could prevent that an object in C could have two possible forms. Question 2: What about the same problem in a symmetric monoidal closed category ? Here things are a bit more complicated, since the bifunctor x no longer is a product and there are no decomposing projection morphisms. In fact, an object which has the form A x (B x C) could be indistingusihable or even identical to an object of the form (A x B) x C. What is known here ? Can an object at the same time be of the form U x V and of the form W => x ?? And what about identifications of products due to assoviativity commutativity and neutrality ? Please reply to cap@ifi.unizh.ch. THANX A LOT FOR YOUR HELP. -- * Prof. Clemens H. CAP cap@ifi.unizh.ch (email) * Dept. of Computer Science +41-1-257 / 4326, 4331 (office voice) * University of Zurich +41-1-363 00 35 (office fax) * Winterthurerstr. 190 +41-1-362 97 11 (home; voice and fax) * CH-8057 Zurich, Switzerland * Motto: "Please do not read the last line of this signature".