Smooth and rough modules over self-induced algebras

Details Smooth and rough modules over self-induced algebras Smooth and rough modules over self-induced algebras

2009-11-19

arxiv.org/abs/0911.3882v1

Mathematics

Rings and Algebras

Scientific paper

A non-unital algebra in a closed monoidal category is called self-induced if the multiplication induces an isomorphism between A\otimes_A A and A. For such an algebra, we define smoothening and roughening functors that retract the category of modules onto two equivalent subcategories of smooth and rough modules, respectively. These functors generalise previous constructions for group representations on bornological vector spaces. We also study the pairs of adjoint functors between categories of smooth and rough modules that are induced by bimodules and Morita equivalence.

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