Rewriting Systems on Arbitrary Monoids
A categorical study of rewriting systems beyond free monoids, including a 2-dimensional account of presentations and generalized extended Tietze transformations.
Mathematician · Logic & categories
Research in model theory, categorical logic and topos theory.
I am Eduardo Magalhães, a PhD researcher at Università degli Studi dell'Insubria. I study how model theory, categorical logic and topos theory illuminate the same mathematical structures from different directions.
- Based in
- Porto → Como
- Current direction
- Categorical stability
01 / Research
Research interests
My research is primarily in model theory and categorical logic, with a particular interest in topos-theoretic methods.
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01
Model theory
The study of mathematical structures through the logical theories they satisfy, with a particular interest in classification questions and stability-theoretic methods.
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02
Categorical logic
Categorical semantics and the relationship between logical theories, their models and interpretations, especially where logical structure is captured by categorical constructions.
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03
Topos theory
Topos-theoretic methods in logic and model theory, and the ways in which geometric and categorical structures offer new perspectives on mathematical theories.
02 / Selected work
Publications & preprints
On Definably Compact Semigroups in o-Minimal Structures
Structural results for definably compact semigroups in o-minimal structures, connecting definable algebra with tools from model theory.
03 / Teaching
Teaching and outreach
My teaching experience includes undergraduate courses at FCUP and student mini-courses in category theory and mathematical logic.
2025 - 2026
Adjunct Assistant Professor
Department of Mathematics · FCUP
Linear Algebra · Abstract Algebra · Real Analysis II
Mar - Jun 2026
Category Theory
Student mini-course · FCUP
Organizer & lecturer
May - Jun 2025
Mathematical Logic & Applications
Student mini-course · FCUP
Organizer & lecturer
04 / Talks
Selected talks and presentations
2026
TACL 2026
Rewriting Systems on Arbitrary Monoids
Topology, Algebra, and Categories in Logic
2025
Mathematical Logic Seminar
Definable Semigroups in o-Minimal Structures
CEMS.UL · University of Lisbon
2025
18th IJUP Meeting
Semigroups Definable in o-Minimal Structures
University of Porto
✦ Best Oral Communication Award05 / Background
Education and academic positions
PhD in Computer Science and Mathematics of Computation
Università degli Studi dell'Insubria · Como, Italy
Supervision: Olivia Caramello
Associate Member
Centro de Matemática da Universidade do Porto (CMUP)
Research affiliation in mathematics.
MSc in Mathematics
Faculdade de Ciências · University of Porto
Thesis: Definable Semigroups in o-Minimal Structures.
Supervision: Mário Edmundo and Jorge Almeida
BSc in Mathematics
Faculdade de Ciências · University of Porto
Contact information
I welcome any conversations about category theory, logic, seminars, teaching and possible collaborations.