Deformation theory of representations of prop(erad)s I

  title={Deformation theory of representations of prop(erad)s I},
  author={S. Merkulov and B. Vallette},
Abstract In this paper and its follow-up [Merkulov and Vallette, J. reine angew. Math.], we study the deformation theory of morphisms of properads and props thereby extending Quillen's deformation theory for commutative rings to a non-linear framework. The associated chain complex is endowed with an L ∞-algebra structure. Its Maurer-Cartan elements correspond to deformed structures, which allows us to give a geometric interpretation of these results. To do so, we endow the category of prop(erad… Expand

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