---
title: "categorical grammar"
type: concept
related: [Category, Categorical Grammar, Grammar, Set]
source: https://www.jemoka.com/posts/kbhcategorical_grammar/
confidence: high
status: active
---

categorical grammar is a grammar in the language of categories.
constituents \(A\), a set of &ldquo;expressions&rdquo; \(C\), a set of categories of &ldquo;syntax&rdquo; \(\varphi: A \to Pow( C)\), 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 &ldquo;3-place&rdquo; 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:
