Dear Aleks I believe André Joyal and I wrote up the non-symmetric case (that is, autonomous monoidal) and it can be found at: http://www.maths.mq.edu.au/~street/PlanarDiags.pdf The strings are piecewise linear in the plane. Smooth strings could be used too. With symmetry, the problem becomes combinatorial as for the case of a symmetric monoidal (tensor) category in The geometry of tensor calculus I, Advances in Math. 88 (1991) 55-112 The geometry of tensor calculus II was going to include the case you want and we probably understood it years ago but that paper is not written. There are delicacies in the tortile monoidal case but not in the symmetric case, it seems to me. Best wishes, Ross On 29/09/2011, at 9:01 PM, Aleks Kissinger wrote:
Categorists,
Everyone (as far as I know) believes that appropriately defined string diagrams can be used to construct the free compact closed category on a monoidal signature. Kelly-Laplaza proved this only for the case of boxes that have a single wire in and out (i.e. free CCC's on a category, not on an arbitrary moniodal signature). However, at least at the time of publishing his survey (2009), Selinger writes that a general proof doesn't exist in the literature. So, my question is:
Is this still the case, and why?
Is it simple a question of someone putting in the hours to write this up, or are there serious technical obstacles to the general result?
Thanks! Aleks Kissinger
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