DEVS (Discrete EVent System) has been proposed to formalize discrete dynamical systems and is widely used for modeling and simulation. Although the operational semantics of DEVS models is well defined, and it exists some attempt to characterize their behavior using temporal logics, there is no attempt to define their denotational semantics. The meaning of a DEVS model is the set of possible coupled input, output and state trajectories. Therefore, denotational semantics is a mapping from DEVS models onto an algebra of trajectories. In this paper, we use category theory to define this algebra. This algebra, called Dyn, is made of trajectories as objects, and the DEVS behavior and structure specifications are mapped onto morphisms between trajectories, exhibiting their coupling. This result opens the way to algebraic manipulations of DEVS models, as well as the access to the results and proof mechanisms available in category theory.