Superalgebras and Superstructures: an overviewReport as inadecuate

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1 Department of Mathematics London, Ontario

Abstract : Let M be a combinatorial and left proper model category, possibly with a monoidal structure. If O is either a monad on M or an operad enriched over M, define a superalgebra in M to be a weak equivalence F : sF → tF such that the target tF is an O-algebra in the usual sense. A classical O-algebra is a superalgebra supported by an isomorphism F. A superstructure F is also a weak equivalence such that tF has a structure, e.g Hodge, twistorial, schematic, sheaf, etc. We build a homotopy theory of these objects and compare it with that of usual O-algebras-structures. Our results rely on Smith-s theorem on left Bousfield localization for combinatorial and left proper model categories.

Keywords : Algebras Hodge structures model categories homotopy theory higher categories

Author: Hugo Bacard -



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