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Modules over Monads and Operational Semantics Hirschowitz, André Hirschowitz, Tom Lafont, Ambroise Operational semantics Category theory 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 ̅λμ-calculus, π-calculus, Positive GSOS specifications, differential λ-calculus, and the big-step, simply-typed, call-by-value λ-calculus. Finally, we design a suitable notion of signature for transition monads. Schloss Dagstuhl – Leibniz-Zentrum für Informatik André Hirschowitz and Tom Hirschowitz and Ambroise Lafont 2020 Is Part Of LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2020.12 urn:nbn:de:0030-drops-123341 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.12 eng https://creativecommons.org/licenses/by/3.0/legalcode