Category analysis: from biochemical mechanics to astrophysics

Full text: One of the main goals of this report is to bridge the gap between computer modelling and group analysis of nonlinear partial differential equations. But we can work with a category of groups rather than a Lie group. In view of the experience of the past development of the relation between mathematics, mechanics and physics, the categorical extension may be justified that one day categoric structures will be as important as groups are today. Also our aim is the application of the same category-theoretic methods in biochemical mechanics and astrophysics. As examples we consider the category analysis of material models for concrete, wood and reinforcing or prestressing steel, on the one hand, and process of the linear and circular polarization of the cosmic microwave background radiation due to the quantum effects of electromagnetic field in anisotropic Bianchi-type cosmological models, on the other hand. (author)