We introduce Rabbit, a combinator-based query language. Rabbit is designed to let data analysts and other accidental programmers query complex structured data. We combine the functional data model and the categorical semantics of computations to develop denotational semantics of database queries. In Rabbit, a query is modeled as a Kleisli arrow for a monadic container determined by the query cardinality. In this model, monadic composition can be used to navigate the database, while other query combinators can aggregate, filter, sort and paginate data; construct compound data; connect self-referential data; and reorganize data with grouping and data cube operations. A context-aware query model, with the input context represented as a comonadic container, can express query parameters and window functions. Rabbit semantics enables pipeline notation, encouraging its users to construct database queries as a series of distinct steps, each individually crafted and tested. We believe that Rabbit can serve as a practical tool for data analytics.