Mathematics

My mein field of research is categorical algebra. More broadly, I am interested in research topics category theory, universal algebra, general topology, order theory, set theory, logic, and combinatorics, as well as applications of mathematics structures beyond mathematics, e.g., in music and human function. My ongoing broad projects that includes research spanning over many years are the following:

• The study of exactness properties: these are properties of categories expressed using limits and colimits. I particularly like to bring in logical and algebraic perspectivew in this area. 
• The study of functors as an extension of the categorical context for dealing with homomorphism theorems in algebra. My contribution here is in using the functorial language for revealing duality. I work particularly with faithful amnestic functors, which I call forms.
• The study of a special type of monoidal categories, called sum structures. These are monoidal structures that behave similarly to coproducts, but are significantly more general than those. In some sense, sum structures are to monoidal structures in a similar relation as forms are to Grothendick fibrations. These two have a common root which link with Grothendieck topologies: cover relations.
• The study of symmetry and of combinatorial objects. I particularly like counting how many partial symmetries does a structure exhibit.
• 2-dimensional categorical algebra: transporting ideas from 1-dimensional categorical algebra to 2-dimensional category theory, and using 2-dimensional category theory for organising concepts in 1-dimensional categorical algebra.
• I like introducing and studying new mathematical structures. In particular, I have worked in this direction in connection with generalising connectivity and vector spaces.
• I am also interested in 1/2-dimensional category theory (i.e, when categories are replaced with ordered sets): in particular, I like to apply it to understand concepts in 1-dimensional category theory (this links with my interest in forms and combinatorics, as well as my interest in connectivity).
• I like logic and set theory. My favorite topics are: ordinal number system, foundations of mathematics, higher-order logic and computer formalisation of mathematics.
• I am interesting in the mathematical structure of musical form as well as the use of mathematics to describe abstractly the structure of human function.
• I am also interested in the study of pedagogy of deductive reasoning.

The list of my publications as well as preprints can be found here.