10 citations · 56 across the 10 of their papers we have counts for
11 papers
The derived category of a generalized complex torus
Patrick Antweiler, Vicente Cortés, Julian Holstein +2
For any translation invariant generalized complex structure J on a torus we construct the derived category D(J) generalizing the derived category of coherent sheaves on a complex t…
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…
Analytification of mapping stacks
Julian Holstein, Mauro Porta
Derived mapping stacks are a fundamental source of examples of derived enhancements of classical moduli problems. For instance, they appear naturally in Gromov-Witten theory and in…
Homotopy theory of monoids and derived localization
Joe Chuang, Julian Holstein, Andrey Lazarev
We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology. This includes a recent generalization of Adams…
Maurer-Cartan moduli and theorems of Riemann-Hilbert type
Joseph Chuang, Julian Holstein, Andrey Lazarev
We study Maurer-Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type,…
The global derived period map
Carmelo Di Natale, Julian V. S. Holstein
Abstract. We develop the global period map in the context of derived geometry, generalising Griffiths' classical period map as well as the infinitesimal derived period map. We begi…
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…
Morita cohomology and homotopy locally constant sheaves
Julian V. S. Holstein
We identify Morita cohomology, which is a categorification of the cohmology of a topological space X, with the category of homotopy locally constant sheaves of perfect complexes on…
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…