Cartesian isomorphisms are symmetric monoidal: A justification of linear logic

Journal of Symbolic Logic 64 (1):227-242 (1999)
Abstract
It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects (i.e., a graph without arrows) can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism
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