FERNANDO LUCATELLI NUNES

Ph.D. in Mathematics Ph.D. in Computer Science

My research spans both pure mathematics and computer science.

In mathematics, I work on the theory and applications of low- and higher-dimensional generalised categorical structures, often developed through two- and three-dimensional universal algebra. This programme connects naturally with areas such as proof theory, the geometry of manifolds, algebraic topology, universal algebra, logic, and related fields.

In computer science, I work in programming language semantics, formal methods, and software technology, with particular emphasis on correctness-by-construction approaches to the design and implementation of programming languages. My research combines rigorous semantic analysis with questions arising from the engineering of modern programming paradigms.

More broadly, I am committed to the systematic use of formal and mathematical structures in computer science and software engineering. I regard structural and logical methods not as external tools, but as foundations for sound design. The aim is to develop coherent theories that guide implementation and yield systems that are reliable, transparent, and conceptually well-founded.

I welcome discussions and collaborations with researchers and prospective PhD students working in categorical structures, programming language theory, formal methods, software technology, or closely related areas. If you would like to explore common interests, please feel free to get in touch.

Published Articles

Lucatelli Nunes, Fernando; Vákár, Matthijs. Monoidal closure of Grothendieck constructions via Σ-tractable monoidal structures and Dialectica formulas. Theory and Applications of Categories, 44(35): 1153-1217. 2025. (65 pages) (arXiv)
Lucatelli Nunes, Fernando; Prezado, Rui; Vákár, Matthijs. Free Extensivity via Distributivity. Portugaliae Mathematica, 82(1–2): 177–204. 2025. (28 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando; Vákár, Matthijs. Automatic Differentiation for ML‑Family Languages: Correctness via Logical Relations. Mathematical Structures in Computer Science, 34(8): 747–806. 2024. (60 pages) (DOI; arXiv)
Prezado, Rui; Lucatelli Nunes, Fernando. Generalized Multicategories: Change‑of‑Base, Embedding, and Descent. Applied Categorical Structures, 32(6): 35. 2024. (89 pages) (DOI; arXiv)
Clementino, Maria Manuel; Lucatelli Nunes, Fernando; Prezado, Rui. Lax Comma Categories: Cartesian Closedness, Extensivity, Topologicity, and Descent. Theory and Applications of Categories, 41(16): 516–530. 2024. (15 pages) (arXiv)
Clementino, Maria Manuel; Lucatelli Nunes, Fernando Lax comma 2‑categories and admissible 2‑functors. Theory and Applications of Categories, 40(06): 180-226. 2024. (47 pages) (arXiv)
Lucatelli Nunes, Fernando; Vákár, Matthijs. CHAD for Expressive Total Languages. Mathematical Structures in Computer Science, 33(4–5): 311–426. 2023. (116 pages) (DOI; arXiv)
Prezado, Rui; Lucatelli Nunes, Fernando. Descent for Internal Multicategory Functors. Applied Categorical Structures, 31(1): 11. 2023. (18 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando; Prezado, Rui; Sousa, Lurdes. Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations. BBMS – Simon Stevin, 30(1): 130–139. 2023. (10 pages) (arXiv)
Clementino, Maria Manuel; Lucatelli Nunes, Fernando. Lax Comma Categories of Ordered Sets. Quaestiones Mathematicae, 46(sup1): 145–159. 2023. (14 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando; Sousa, Lurdes. On Lax Epimorphisms and the Associated Factorization. Journal of Pure and Applied Algebra, 226(12): 107174. 2022. (27 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando. Semantic Factorization and Descent. Applied Categorical Structures, 30: 1393–1433. 2022. (41 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando. Descent Data and Absolute Kan Extensions. Theory and Applications of Categories, 37: 530–561. 2021. (32 pages) (arXiv)
Lucatelli Nunes, Fernando. Pseudoalgebras and non‑canonical isomorphisms. Applied Categorical Structures, 27(1): 55–63. 2019. (9 pages) (DOI; arXiv)
Lucatelli Nunes, Fernando. Pseudo‑Kan Extensions and Descent Theory. Theory and Applications of Categories, 33(15): 390–444. 2018. (35 pages) (arXiv)
Lucatelli Nunes, Fernando. On lifting of biadjoints and lax algebras. CGASA, 9(1): 29–58. 2018. (30 pages)(arXiv)
Lucatelli Nunes, Fernando. On Biadjoint Triangles. Theory and Applications of Categories, 31(9), 217-256. 2016. (40 pages) (arXiv)

Submitted / Under Review / Preprints

Lucatelli Nunes, Fernando; Plotkin, Gordon; Vákár, Matthijs. Unraveling the iterative CHAD. Preprint. arXiv:2505.15002. 2025. (57 pages)
Lucatelli Nunes, Fernando; Vákár, Matthijs. Free Doubly‑Infinitary Distributive Categories are Cartesian Closed. Preprint. arXiv:2403.10447. 2024. (16 pages)
Lucatelli Nunes, Fernando; Prezado, Rui. Functors Preserving Effective Descent Morphisms. Preprint. arXiv:2410.22876. 2024. (17 pages)
Lucatelli Nunes, Fernando. Freely generated n-categories, coinserters and presentations of low dimensional categories. Preprint. arXiv:1704.04474. 2017. (56 pages)

Workshop and other publications

Lucatelli Nunes, Fernando. Pseudomonads and Descent . University of Coimbra, 2017. (209 pages)
Lucatelli Nunes, Fernando; Vákár, Matthijs. Logical Relations for Partial Features and AD Correctness. Oberwolfach Preprints (OWP-2023-09). Preprint. arXiv:2210.08530. 2022. (21 pages)
Lucatelli Nunes, Fernando; Plotkin, Gordon; Vákár, Matthijs. Homomorphic Reverse Differentiation of Iteration. LAFI 2024 (Tenth Workshop on Languages for Inference at POPL, 2024).(2 pages)
Lucatelli Nunes, Fernando. Non-reversible spaces (in Portuguese). Revista Matemática Universitária , 48-49. 2010. (5 pages)

Undergraduate and Graduate Monographs

Lucatelli Nunes, Fernando. Basic Concepts of Topology for Topological Dynamics (in Portuguese) . 2009. (116 pages)
Lucatelli Nunes, Fernando. Basic Topological Dynamics and Basic Applications to Number Theory (in Portuguese). 2009. (57 pages)