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<a href="../conf.html">Symmetry in Nonlinear Mathematical Physics - 2009
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<i>Yuri Bespalov</i> (Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine)



<p><b><font size=+2>Natural factorizations and related categorical structures</font></b>
<p><b>Abstract:</b>
<br>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.
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