Index

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. I am a postdoctoral researcher at the University of Oxford, working with Sam Staton. Previously, I was a PhD student at the Compositional Systems and Methods Group, working with Pawel Sobocinski.

• ArXiv, GitHub, CV.

Preprints

• 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.

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

Publications

• Order in Partial Markov Categories.
  Elena Di Lavore, Mario Román, Pawel Sobocinski, Márk Széles.
  (pdf), To appear at MFPS 2025.

• Effectful Mealy Machines: Bisimulation and Trace
  Filippo Bonchi, Elena Di Lavore, and Mario Román.
  (arXiv, notes), to appear at ACM/IEEE Symposium on Logic in Computer Science (LiCS 2025).

• String Diagrams for Premonoidal Categories.
  Mario Román and Pawel Sobocinski.
  (arXiv, LMCS) 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) ACM/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.
  (arXiv, slides) ACM/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.
  (arXiv, notes) Applied Category Theory (ACT 2022).

• Open Diagrams via Coend Calculus.
  Mario Román.
  (arXiv, 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.
  (arXiv, 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.
  (JOSE) Journal of Open Source Education, 2018.

PhD Thesis

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

Extended abstracts

• Timing via Pinwheel Double Categories (preprint), with Elena Di Lavore.
• 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).

Talks

• 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 Pisa CS Department Seminar, 2024.
• Notes on profunctors, at the PUDDLE seminar, Oxford, 2024.
• Effectful Streams, at CMCS’24, Luxembourg.
• Polar Shuffles, at the CHESS-PTSPC’24 workshop, Tallinn.
• The Produoidal Algebra of Process Decomposition, at CSL24, 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.

Curriculum

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.

• ARIA invited event, Safeguarded AI — Nottingham, 7-11 April, 2025.
• 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 — Palmse, 2020.
• Nordic Workshop on Programming Theory — Tallinn, 2019.
• Category Theory Conference — Edinburgh, 2019.
• Applied Category Theory Adjoint School, 2019.

Notes

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: do please contact me by email if you want to discuss or comment on any. You may want read about monoidal categories, profunctors, or duoidal categories, or to use the search box (Ctrl+K) to jump to any topic.