My research is in algebra, category theory, categorical algebra, universal algebra, and algebraic logic.
I am mainly interested in categorical methods in algebra: how algebraic structures can be studied through their intrinsic categorical properties, and how algebraic examples suggest new categorical notions.
Much of my work is related to semi-abelian and homological categories, protomodularity, internal groupoids, crossed modules, butterflies, normality, actions, and torsion-theoretic phenomena. I am also interested in categorical aspects of algebraic logic, including structures related to MV-algebras, lattice-ordered groups, hoops, and valuation-like invariants.
Categorical algebra and homological methods
A central part of my research concerns algebraic and homological structures in categorical contexts. This includes semi-abelian categories, homological categories, Mal’tsev and protomodular categories, normal subobjects, equivalence relations, commutators, internal groupoids, and crossed modules.
Several of my papers deal with internal categorical structures and their homological behaviour, including exact sequences of higher groupoids, internal crossed modules, Peiffer commutators, normal monomorphisms, relative ideals, and categorical forms of obstruction theory.
Butterflies, crossed modules, and higher-dimensional algebra
Another recurring theme is the use of butterflies and related structures to understand morphisms, extensions, and cohomological constructions in non-abelian and semi-abelian settings.
This line of work includes the calculus of butterflies, the snail lemma, cohomology 2-groups, groupal pseudofunctors, and fibred-categorical obstruction theory.
Protomodularity and universal algebra
I am interested in the interaction between categorical properties and universal algebraic structure. In particular, I study protomodular varieties and prevarieties, algebraic theories, and the way categorical conditions such as finite completeness, normality, and conservativity of change-of-base functors reflect algebraic phenomena.
Algebraic logic
Part of my recent work concerns algebraic and categorical structures arising from logic, especially MV-algebras, hoops, Heyting semilattices, lattice-ordered groups, and related categorical constructions.
I am particularly interested in universal properties, evaluation-like invariants, and the categorical meaning of classical algebraic representations such as the Mundici equivalence.
Research projects and affiliations
I am a member of GNSAGA, the National Research Group in algebraic structures and combinatorial geometry of INdAM.
I am a co-founder and member of the steering committee of ItaCa, the Italian community of category theorists, which runs seminars, workshops, online courses, and other scientific activities.
In 2023 I was head of the Palermo research unit of the PRIN PNRR project “Quantum Models for Logic, Computation and Natural Processes”.