Categorical grammar is a type of formal grammar that uses categories to describe the structure of sentences. It focuses on how words and phrases can be grouped based on their grammatical roles, such as nouns, verbs, and adjectives. This approach helps in understanding the relationships between different parts of a sentence. In categorical grammar, each category is associated with specific rules that dictate how elements can combine. This framework is often linked to type theory and lambda calculus, which are used in fields like linguistics and computer science to analyze language and develop programming languages.