We introduce the Functor Model, a deterministic framework for artificial intelligence in which models are defined as structure-preserving mappings over equivalence classes of inputs. By collapsing redundant representations via canonicalization, the model potentially eliminates unnecessary computation while preserving task outcomes. We formalize inference, learning, and equivalence under this framework, define atomic update semantics, and discuss a model-internal energy bound for equivalent AI operations under standard assumptions. The Functor Model provides a mathematically grounded alternative to stochastic parameter-based learning, emphasizing determinism, stability, and efficiency. Although Functor Models are internally deterministic, while presenting externally as probabilistic systems through explicit, governed semantics that can emulate stochastic model behavior for supported problem classes. Live demo of micro at https://api.functormodel.ai/functor-demo. Patent pending.