categorical grammar is a grammar in the language of categories. constituents A, a set of “expressions” C, a set of categories of “syntax” \varphi: A \to Pow( C), assigning each a \in A to a set of categories c \subset C G: a family of sets of n-place operations where n=1, 2, \ldots (what does a “3-place” op mean? idk) R: a set of rules encoded as tuples: (f; \{c_1, \dots c_{k}\}; c_{k+1}), where f is a k place operation, and c_{j} \in C requirements The operations of this grammar behaves like so: given a rule r \in R, it tells you that given WLOG an expression in c_{1}, c_2, \ldots c_{k} \in C (i.e. they were mapped to that set \varphi), f will map that set of expressions into the same new category c_{k+1}. additional information a basic categorical grammar one implementation of a basic categorical grammar is as follows: