Homological and Homotopical Algebra

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Algebra & Geometry. Homological and homotopical algebra is a spectacular area of Mathematics with many applications within and around mathematics. One of the ingenious discoveries were made by V Voevodsky, who was awarded the Fields medal in 2002. His work lead top solution of a number of longstanding problems with far reaching implications. Very recently, Dr G Garkusha and I Panin have accomplished a programme of Voevodsky, which began in 2001. G Garkusha and I Panin use enriched motivic homotopy theory. The project is to explore and develop further aspects of the enriched homotopy theory and enriched homological algebra which is of major importance in Garkusha-Panin's theory. Applications are expected in motivic homotopy theory, ring and module theory, homological algebra..