Abelian Categories of Modules over a (Lax) Monoidal Functor

Details Abelian Categories of Modules over a (Lax) Monoidal Functor Abelian Categories of Modules over a (Lax) Monoidal Functor

2001-12-29

arxiv.org/abs/math/0112307v1

Mathematics

Category Theory

Scientific paper

The analogy between Yetter's deformation theory form (lax) monoidal functors and Gerstenahaber's deformation theory for associative algebras is solidified by shown that under reasonable conditions the category of functors with an action of a lax monoidal functor is abelian, that an analogue of the Hochschild cohomology of an algebra with coefficients in a bimodule exists for monoidal functors, and is given by right derived functors. The deformation cohmology of a monoidal natural transformation is shown to be a special case.

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