Modelling natural language in some form is a core motivation for computational linguists and logicians, and more recently big tech firms which favour (often very impressive) engineering solutions over rigour. Compositional-distributional models of meaning combine rigorous models of grammar, in the form of Lambek calculus, and modern NLP models, forming a framework for model meaning using structure and statistics. This framework can be neatly specified using category theory which connects sequent calculus, residuated monoids and pregroups as well as surprising links to quantum informatics.