On Homological and Homotopical Algebra of Supersymmetries and   Integrability in String Theory
  The text contains introduction and preliminary definitions and results to my talk on category theory description of supersymmetries and integrability in string theory. In the talk I plan to present homological and homotopical algebra framework for Calabi-Yau supermanifolds and stacks in open and closed string theory. In the framework we investigate supersymmetries and integrability. 
Nikolaj M. Glazunov