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Modules and Morita theorem for operads
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 123, Number 5, October 2001
- pp. 811-838
- 10.1353/ajm.2001.0033
- Article
- Additional Information
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Associative rings A, B are called Morita equivalent when the categories of left modules over them are equivalent. We call two classical linear operads P, Q Morita equivalent if the categories of algebras over them are equivalent. We transport a part of Morita theory to the operadic context by studying modules over operads. As an application of this philosophy, we consider an operadic version of the sheaf of linear differential operators on a (super)manifold M and give a comparison theorem between algebras over this sheaf on M and Mred.