Graphical Presentations of Symmetric Monoidal Closed Theories

Richard Garner (1, 2) , Tom Hirschowitz (3) , Aurélien Pardon (4)

1 DPMMS - Department of Pure Mathematics and Mathematical Statistics
2 Uppsala University
3 LAMA - Laboratoire de Mathématiques
4 LIP - Laboratoire de l'Informatique du Parallélisme

We define a notion of symmetric monoidal closed (SMC) theory, consisting of a SMC signature augmented with equations, and describe the classifying categories of such theories in terms of proof nets.

Mots clés: Symmetric monoidal closed categories; Coherence; Proof nets

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Richard Garner, Tom Hirschowitz, Aurélien Pardon. Graphical Presentations of Symmetric Monoidal Closed Theories. 2008. ⟨hal-00333750v2⟩