10 citations · 56 across the 10 of their papers we have counts for
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Hochschild cohomology of the second kind: Koszul duality and Morita invariance
Ai Guan, Julian Holstein, Andrey Lazarev +1
We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category. The Hochschild cohomology o…
Enriched Koszul duality for dg categories
Julian Holstein, Andrey Lazarev
It is well-known that the category of small dg categories dgCat, though it is monoidal, does not form a monoidal model category. In this paper we construct a monoidal model structu…
Categorical Koszul duality
Julian Holstein, Andrey Lazarev
In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for dg algebras and conilpotent curved coalg…
Explicit homotopy limits of dg-categories and twisted complexes
Jonathan Block, Julian V. S. Holstein, Zhaoting Wei
In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show tha…
Properness and simplicial resolutions for the model category dgCat
Julian V. S. Holstein
We provide proofs of two properties of the model category dgCat of dg-categories (with the Morita or Dwyer-Kan model structure): When working over a field the category dgCat is lef…