Symmetric monoidal sketches

We introduce and develop the notion of symmetric monoidal sketch. Every symmetric monoidal sketch generates a generic model. If the sketch is commutative and single-sorted, the generic model can be characterised as a free structure on 1, and the construction sending a small symmetric monoidal category to the category of models of the sketch in it can be seen as a right adjoint. We investigate specific cases generated by the Eckmann-Hilton argument, which allows a simple characterisation of the constructions. This accounts for the various categories of wiring currently being investigated in modelling concurrency, as well as providing a basis for understanding the axiomatically generated categories in axiomatic domain theory and in presheaf models of concurrency.

• Type: Conference
• Year: 2000
• Where: PPDP
• Authors: Martin Hyland, John Power
• Keywords: Generic Model, PPDP 2000, Programming Languages, Symmetric Monoidal, Symmetric Monoidal Sketch