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André-Quillen cohomology in the context of curved algebras
Joan Bellier-Millès, Sinan Yalin
The André-Quillen cohomology of an algebra with coefficients in a module is defined by deriving a functor based on Kähler differential forms. It can be computed using a cofibrant r…
Homotopy theory of curved operads and curved algebras
Joan Bellier-Millès, Gabriel C. Drummond-Cole
Curved algebras are algebras endowed with a predifferential, which is an endomorphism of degree -1 whose square is not necessarily 0. This makes the usual definition of quasi-isomo…
Operads with compatible CL-shellable partition posets admit a Poincaré-Birkhoff-Witt basis
Joan Bellier-Millès, Bérénice Delcroix-Oger, Eric Hoffbeck
In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of be…