We propose that axiomatization in physics is a specific sort of mathematically conscientious and empirically mindful systematic organization of a physical theory describing a specific domain of physical systems and phenomena. It is shown how such a notion of axiomatization can be specified using category theory. Suitable concepts of completeness and categoricity of the proposed axiomatization are defined and discussed. The axiomatization is illustrated on the example of non-relativistic quantum mechanics of finite degrees of freedom. It is argued that if the suggested notion of axiomatization in physics is accepted as manifestation of rigour in physics, then rigour is not a single property but a structured notion.
Motivated by Hilbert's sixth problem on axiomatization of physics, the author is proposing a rather provocative abstract axiomatic framework called S - formalization, where S is an arbitrary physical system .The proposal is an attempt to provide a general axiomatic framework , from which mathematical frameworks of new physical theories can be formulated on firm axiomatic basis and the mathematical frameworks of subjects such as standard (nonrelativistic) quantum mechanics are naturally derived as special cases of this general axiomatic framework. Introduction