Abstract. Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds ing the level of abstraction of the resulting semantics. The classifications are formalized through the medium of category theory. Keywords. Semantics, Concurrency, Models for Concurrency, Categories. Contents 1 Preliminaries 431 2 Deterministic Transition Systems 433 3 Noninterleaving vs. Interleaving Models 436 Synchronization Trees and Labelled Event Structures . . . . . . . . . . . . . . 438 Transition Systems with Independence . . . . . . . . . . . . . . . . . . . . . . 439 4 Behavioural, Linear Time, Noninterleaving Models 441 Semilanguages and Event Structures . . . . . . . . . . . . . . . . . . . . . . . 443 Trace Languages and Event Structures . . . . . . . . . . . . . . . . . . . . . . 446 5 Transition Systems with Independence and Labelle...