Categorial Grammar is a type of formal grammar that uses categories to describe the syntactic structure of sentences. It assigns categories to words and phrases, indicating their grammatical roles, such as nouns, verbs, and adjectives. This approach helps in understanding how different parts of a sentence combine to form meaningful expressions. In Categorial Grammar, each category has specific rules for combining with other categories, often represented using arrows. For example, a verb phrase might be categorized as a function that takes a noun phrase as input and produces a sentence. This framework is useful in fields like linguistics and computational linguistics.