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- W2214238599 abstract "An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:mathcal{O}rightarrowmathcal{P}$ describes a functor allowing a $mathcal{P}$-algebra to be viewed as an $mathcal{O}$-algebra. We show that the $mathcal{O}$-algebra (co)homology of a $mathcal{P}$-algebra may be represented by a certain operadic comodule. Thus filtrations of this comodule result in spectral sequences computing the (co)homology. As a demonstration we study operads with a filtered distributive law; for the associative operad we obtain a new proof of the Hodge decomposition of the Hochschild cohomology of a commutative algebra. This generalises to many other operads and as an illustration we compute the post-Lie cohomology of a Lie algebra." @default.
- W2214238599 created "2016-06-24" @default.
- W2214238599 creator A5060829874 @default.
- W2214238599 date "2014-03-19" @default.
- W2214238599 modified "2023-09-27" @default.
- W2214238599 title "Operadic comodules and (co)homology theories" @default.
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