Mario Román

Research Associate.
Department of Computer Science, University of Oxford.
Room 309, Wolfson Building, Parks Road.
Oxford, OX1 3QD.
mromang08@gmail.com

My research is in category theory, functional programming, foundations for probabilistic programming, formal languages, and mathematical notation.

• ArXiv, GitHub, CV.

• Partial Markov Categories
  Elena Di Lavore, Mario Román, and Pawel Sobocinski.
  (arXiv), Preprint, 2025.

• A Simple Formal Language for Probabilistic Decision Problems
  Elena Di Lavore, Bart Jacobs, and Mario Román.
  (arXiv), Preprint, 2024.

• Effectful Mealy Machines: Bisimulation and Trace
  Filippo Bonchi, Elena Di Lavore, and Mario Román.
  (arXiv), Preprint, 2024.

• Coinductive Monoidal Streams.
  Elena Di Lavore, Giovanni de Felice, and Mario Román.
  (arXiv), Preprint, 2023.

• String Diagrams for Premonoidal Categories.
  Mario Román and Pawel Sobocinski.
  (arXiv) Logical Methods in Computer Science (LMCS), 2025.

• Context-Free Languages of String Diagrams
  Matt Earnshaw and Mario Román.
  (pdf) Foundations of Software Sc. and Computation Struct. (FoSSaCS 2025).

• The Produoidal Algebra of Process Decomposition.
  Matt Earnshaw, James Hefford, and Mario Román.
  (pdf, notes) Computer Science Logic (CSL 2024).

• Collages of String Diagrams.
  Dylan Braithwaite and Mario Román.
  (pdf, arXiv) Applied Category Theory (ACT 2023).

• Evidential Decision Theory via Partial Markov Categories.
  Elena Di Lavore and Mario Román.
  (pdf, slides, notes) IEEE Symposium on Logic in Computer Science (LiCS 2023).

• Optics for Premonoidal Categories.
  James Hefford and Mario Román.
  (arXiv) Applied Category Theory (ACT 2023).

• Monoidal Streams for Dataflow Programming.
  Elena Di Lavore, Giovanni de Felice, and Mario Román.
  (pdf, slides) IEEE Symposium on Logic in Computer Science (LiCS 2022), Distinguished, Kleene Award.

• Span(Graph): a Canonical Feedback Algebra of Open Transition Systems.
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  (pdf) Software and Systems Modeling, Volume 22, pages 495–520 (2023).

• A Canonical Algebra of Open Transition Systems.
  Elena Di Lavore, Alessandro Gianola, Nicoletta Sabadini, Mario Román, and Pawel Sobocinski.
  (pdf) Formal Aspects of Component Software (FACS 2021).

• Promonads and String Diagrams for Effectful Categories.
  Mario Román.
  (pdf, notes) Applied Category Theory (ACT 2022).

• Open Diagrams via Coend Calculus.
  Mario Román.
  (pdf, notes) Applied Category Theory (ACT 2021).

• Cornering Optics.
  Guillaume Boisseau, Chad Nester, and Mario Román.
  (pdf, notes) Applied Category Theory (ACT 2022).

• Profunctor Optics: a Categorical Update.
  Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, and Mario Román.
  (pdf, notes) Compositionality, Volume 6, Issue 1 (2024).

• Profunctor Optics and Traversals.
  Mario Román.
  (pdf) MFoCS thesis, University of Oxford (2019).

• Mikrokosmos: an Educational Lambda Interpreter
  Supervised by Pedro García-Sánchez.
  (pdf) Journal of Open Source Education (JOSE), 2018.

• Monoidal Context Theory.
  Supervised by Pawel Sobocinski.
  (pdf, notes) Tallinn University of Technology, 2023.

• Graded Coalgebras of Monads for Continuous Dynamics (preprint), with Elena Di Lavore.
• Solving Puzzles in Decision Theory (preprint), with Elena Di Lavore.
• String Diagrams for Physical Duoidal Categories (preprint), with Nayan Rajesh.
• Evidential Decision Theory via Partial Markov Categories (NWPT 2024), with Elena Di Lavore.
• Universal Properties of Asynchronous Message Passing (abstract), with Matt Earnshaw.
• Effectful Trace Semantics via Effectful Streams (preprint), with Filippo Bonchi and Elena Di Lavore.
• Coinductive Streams in Monoidal Categories (arXiv), with Elena Di Lavore and Giovanni de Felice.
• Polar Interleavings for Deadlock-Free Message-Passing (preprint), with Matt Earnshaw and Chad Nester.
• Symmetric monoidal automata (preprint), with Elena Di Lavore.
• Presentations of Premonoidal Categories by Devices (preprint), with Matt Earnshaw and Chad Nester.
• Contouring Prostar Autonomous Categories (preprint), with Matt Earnshaw and James Hefford.
• Be Careful with Duoidal Coherence (preprint).
• Coalgebraic Stochastic Continuous Systems (preprint).
• Comb Diagrams for Discrete-Time Feedback (preprint).
• Timing monoidal lax categories (preprint).
• Distributive laws of promonads (preprint).
• Composing optics (preprint).

• String Diagrams for Premonoidal Categories, at the theory seminar, Birmingham, March 2025.
• Partial Markov Categories, at the Computing Markov workshop, Tallinn, February 2025.
• Partial Markov Categories, at the LIS seminar, Aix-Marseille, December 2024.
• Partial Markov Categories, at the LIP seminar, ENS Lyon, December 2024.
• Partial Markov Categories, at the Topos Colloquium, 30 October 2024.
• String Diagrams for Premonoidal Categories, at the CS seminar, Pisa.
• Notes on profunctors, at the PUDDLE seminar, Oxford.
• Effectful Streams, at CMCS'24, Luxembourg.
• Polar Shuffles, at the CHESS-PTSPC'24 workshop, Tallinn.
• The Produoidal Algebra of Process Decomposition, at CSL'24, Naples.
• Notes on Fox’s theorem, at a Tallinn retreat, Matsalu park.
• Polar Interleavings, at NWPT'23, Västerås.
• Monoidal Context Theory, PhD Defence, Tallinn.
• Collages of String Diagrams, at ACT'23, Maryland.
• Timing Processes, at the Bob Walters Tribute 2023, Tallinn.
• Optics: the Algebra of Monoidal Context, at MFPS'23, Bloomington, Indiana.
• The Produoidal Algebra of Process Decomposition, at the Ottawa Logic Seminar.
• From theories to categories at the Lawvere Memorial Meeting, Tallinn.
• String diagrams of string diagrams at TallCat group meetings, Tallinn.
• Evidential Decision Theory via Partial Markov Categories at NWPT'22, Bergen.
• Premonoidal Streams, at the Intercats Seminar of the Topos Institute.
• Monoidal Streams for Dataflow Programming, at LiCS'22.
• Monoidal Streams for Dataflow Programming, at NWPT'21, Reykjavik.
• Notes on A Graphical View at TallCat Seminar, Tallinn.
• Monoidal Streams for Dataflow Programming, at the Bath Mathematical Foundations Seminar.
• Promonads and String Diagrams for Effectful Categories at ACT'22, Strathclyde.
• Notes on Compositional Markov Processes at the ACT'22 Adjoint School, Strathclyde.
• Monoidal Profunctors at Compositional Methods Retreat, Raudsilla.
• A Canonical Algebra of Transition Systems at ACT'21, Cambridge.
• A Canonical Algebra of Transition Systems at FACS'21, Grenoble.
• Picturing Multivariable Adjunctions, the 2-Chu construction at TallCat Seminar, Tallinn.
• Lesson on Monoidal Categories at the Category Theory course, Tallinn.
• Open Diagrams via Coend Calculus at ACT'20, MIT.
• Profunctor Optics: a Categorical Update at ACT'20, MIT.
• Profunctor Optics: a Categorical Update at NWPT'19, Tallinn.
• Profunctor Optics: a Categorical Update at SYCO 5, Birmingham.
• Profunctor Optics: a Categorical Update at MFoCS Dissertation, Oxford.

Positions.

• Research Associate, University of Oxford (2024), supervisor Sam Staton.
• PhD, Tallinn University of Technology (2023), supervisor Pawel Sobocinski.
• MSc, University of Oxford (2019), Foundations of Mathematics and Computer Science.
• BSc, University of Granada (2018), BSc Mathematics.
• BSc, University of Granada (2018), BSc Computer Engineering.

Grant writing.

• ARIA Safeguarded AI, PI: Sam Staton, “Categorical Probability Towards Safe AI” (2024).
• ARIA Safeguarded AI, PI: Pawel Sobocinski, “String Diagrams for Probabilistic Logic” (2024).
• ARIA Safeguarded AI, PI: Filippo Bonchi, “Monoidal Coalgebraic Metrics” (2024).
• Short Term Scientific Mission, “Type theory for exact and continuous Bayesian observations” (2024).
• Short Term Scientific Mission, “Bidimensional Markov Categories” (2024).

Community.

• Executive Board, Compositionality Journal (2023).
• Programme Committee, Applied Category Theory (2024).
• Programme Committee, Applied Category Theory (2023).
• Programme Committee, Applied Category Theory (2022).
• Local Organizer, Applied Category Theory (Oxford, 2024).
• Local Organizer, Mathematical Foundations of Programming Semantics (Oxford, 2024).
• Local Organizer, Mathematical Foundations of Computer Science (Tallinn, 2021).
• Journal Reviewer, Logical Methods in Computer Science (LMCS).
• Journal Reviewer, Mathematical Structures in Computer Science (MSCS).
• Journal Reviewer, Compositionality journal (Compositionality).
• Reviewer, Principles of Programming Languages (POPL'25).
• Reviewer, Logic in Computer Science (LiCS20, LiCS22, LiCS23, LiCS25).
• Reviewer, Applied Category Theory (ACT20, ACT21, ACT22, ACT23, ACT24).
• Reviewer, Symp. Compositional Structures (SYCO6, SYCO7, SYCO8, SYCO9).
• Reviewer, Computer Science Logic (CSL23).
• Reviewer, Foundations of Software Science (FoSSaCS22).
• Reviewer, Coalgebraic Methods in Computer Science (CMCS24).
• Reviewer, Trends in Computer Science (SOFSEM2023).
• Reviewer, Knowledge Representation and Reasoning (KR2023).

Distinctions.

• Kleene Award, “Monoidal Streams for Dataflow Programming”, LiCS'22.
• Invited Talk, “Monoidal Optics are Universal”, special session MFPS'23.
• Distinguished Paper, “Monoidal Streams for Dataflow Programming”, LiCS'22.
• Distinguished Talk, “Effectful Trace Semantics”, ACT'24.
• Distinguished Talk, “Evidential Decision Theory via Partial Markov Categories”, ACT’23.
• Distinguished Talk, “Monoidal Streams for Dataflow Programming”, ACT’22.
• Distinguished Talk, “Profunctor Optics: a Categorical Update”, ACT’20.
• Best BSc thesis, Spanish Royal Mathematical Society, “Category Theory and Lambda Calculus”, 2018.
• Undergraduate Reserch, Fellowship at the Department of Algebra, “Educational λ-calculus interpreter”, 2018.
• International Mathematical Olympiad, Honorary mention, national gold medal, 2012.

Teaching.

• TA for the Applied Category Theory Adjoint School, Glasgow, under Nicoletta Sabadini, 2022.
• TA for Category Theory, Tallinn University of Technology, under Pawel Sobocinski, 2020.
• TA for Functional Programming, Tallinn University of Technology, under Edward Morehouse, 2020.

Visits & Workshops.

• Computing with Markov Categories — Tallinn, 26 February, 2025.
• Tallinn University of Technology — visit, 16-28 February, 2025.
• ARIA invited event, Safeguarded AI ­— York, 4-7 February, 2025.
• Aix-Marseille University — visit, December 2024.
• ENS Lyon — visit, December 2024.
• National Institute of Informatics, Tokyo — visit, 18–22 November, 2024.
• Tallinn University of Technology — visit, 30 October – 14 November, 2024.
• Tallinn University of Technology — visit, 15-30 September, 2024.
• ARIA invited event Safeguarded AI — Manchester, 1–4 October, 2024.
• ARIA invited event Safeguarded AI — Birmingham, 4–5 March 2024.
• University of Pisa — visit, 2024.
• Tallinn University of Technology — CHESS-PTSPC'24 workshop, March 2024.
• Finding the Right Abstractions Workshop 2023, Oxford.
• Finding the Right Abstractions Workshop 2023, San Francisco.
• University of Insubria — visit, 2022.
• Logic in Computer Science 2023, Boston.
• Logic in Computer Science 2022, Haifa.
• Applied Category Theory 2024, Oxford.
• Applied Category Theory 2023 — Maryland, 31 July – 4 August 2023.
• Applied Category Theory 2022, Glasgow.
• Estonian Winter School in Computer Science, 2020.
• Applied Category Theory Adjoint School, 2019.

I collect and hyperlink the notes I write while studying or developing any topic. They are not meant to be definitive and many of them do not contain original material. Think of these as atomic ideas that I am happy to share and discuss. You may want read about monoidal categories, profunctors, or duoidal categories, or to use the search box to jump to any topic. Feedback is welcome.