Research Biography

My professional activity began in mechanical engineering with computing and analysis of strength/deformation fields in railway cars. To balance the concrete nature of this business, I gradually moved to pure mathematics and even to meta-mathematics, trying to understand the very foundations: set theory and logic upon which mathematics is built (a couple of papers can be found here). However, the abstract atmosphere of the foundations turned out too rarified for a former mechanical engineer, and I made a new turn: moved to computer science (and back to industry) to work in a project on view integration and database design. Despite the logic-based nature of software engineering (especially in comparison to mechanical engineering), the abundance of syntactical and terminological forms with little (if any) precise semantics made my first years in computer science really hard. A reminiscence of that can be found here).

 

My life in the database world became much easier when I discovered that the abstract patterns of mathematical category theory (CT) can be quite adequate for modeling many artifacts in software engineering. Understanding the universe to be specified as a topos-like structure of variable sets and, correspondingly,
  • ER-diagrams and similar notations as (generalized) categorical sketches,
  • their instances as sketch mappings into semantic categories (a la model toposes),
  • query languages as monads, databases as algebras and
  • views as Kleisli mappings

provided a consistent mathematical framework, in which the contents of many papers written on these subjects could be compactly presented in a precise way. The approach at once, like a magic key, opened new horizons and made it possible to advance a few difficult issues in knowledge representation and metadata management (particularly, the infamous problem of view/schema integration). The first impression was so strong and exciting that together with Boris Kadish we wrote a propagandistic Manifesto.

 

Of course, time cooled down emotions and placed our predictions into a more realistic framework. Yet I was never disappointed with the fruitfulness of applying categorical ideas to software engineering problems. A few years of working in an industrial environment as a business analyst/modeler, convinced me of the extreme practical usefulness of formulating the problems to be solved in an abstract way. Certainly, this idea has nothing to do specifically with CT: viewing things abstractly (in terms of abstract sets, mappings and relations)  is just a normal mathematical practice. However, the universes to be dealt with in business/enterprise modeling and their software models are built from sets and mappings, and from mappings between these primary universes, and from mappings between these mappings and so on.  Categorical concepts appear here quite naturally as seemingly the only way to precisely specify and manage these wild mapping forests. Moreover, sometimes categorical patterns and software models are such a good match that we can well say that software engineers themselves rediscover and implicitly use categorical patterns (some examples can be found here).

 

Though CT is extremely elegant mathematically, I rarely had a chance to study or work with it in a pure mathematical context. I was usually motivated to understand different pieces of CT by practical problems I was dealing with.   Over years, this practice-guided (it may be better to say practice-forced) journey through CT outlined some territory including categorical logic, categorical algebra and coalgebra, and fibrations (which seem to be everywhere in software engineering). It is exciting to see how these abstract constructions reappear again and again in software engineering models and languages.

A more detailed list of interests can be found in the Publication page.

 

 

 

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