Unfinished draft, October 6, 2004.

This paper links deep inference proof theory, as studied by Guglielmi
*et al.*, to categorical proof theory in the sense of Lambek *et al.*.
It observes how deep inference proof theory is categorical proof
theory, minus the coherence diagrams/laws. Coherence yields a
ready-made and well studied notion of equality on deep inference
proofs.
The paper notes a precise correspondence between the symmetric deep
inference system for multiplicative linear logic (the linear fragment
of **SKSg**) and the presentation of
*-autonomous categories as symmetric linearly distributive categories
with negation. Contraction and weakening in **SKSg** corresponds
precisely to the presence of (co)monoids.