Symmetry in Nonlinear Mathematical Physics - 2009

Yuri Bespalov (Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine)

Natural factorizations and related categorical structures

The basic notion of the homotopy theory is a Quillen's model category. A model structure assumes distinguished classes of morphisms which form two weak factorization systems. Recently discovered concept of a natural weak factorization [M. Grandis, W. Tholen, 2006], [R. Garner, 2007] open a promising possibility to algebraization of the whole subject. We consider some steps towards application of natural factorizations in the context of model categories and relations of these new ideas with the category theory itself.