In monoidal abelian categories with enough right-flat projectives, the co-Hochschild complex of the unit's projective resolution carries a B_infinity-structure that is A_infinity-quasi-isomorphic to the derived endomorphism algebra of the unit and recovers the Hochschild complex for bimodules.
A k-linear triangulated category without a model
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abstract
In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triangulated categories without a model have been constructed by Muro, Schwede and Strickland. These examples are however not linear over a field.
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The $B_\infty$-structure on the derived endomorphism algebra of the unit in a monoidal category
In monoidal abelian categories with enough right-flat projectives, the co-Hochschild complex of the unit's projective resolution carries a B_infinity-structure that is A_infinity-quasi-isomorphic to the derived endomorphism algebra of the unit and recovers the Hochschild complex for bimodules.