Authors: André Hirschowitz ; Tom Hirschowitz ; Ambroise Lafont

This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, and the big-step, simply-typed, call-by-value lambda-calculus. Moreover, we design a suitable notion of signature for transition monads.