47 citations · 357 across the 42 of their papers we have counts for
17 papers · 1 filter
Review of deformation theory II: a homotopical approach
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich, Manetti and Pridham. In particular, we show that any deformation f…
Homological epimorphisms and homotopy epimorphisms
Joe Chuang, Andrey Lazarev
We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a character…
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,…
Cocommutative coalgebras: homotopy theory and Koszul duality
J. Chuang, A. Lazarev, Wajid Mannan
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteris…
Disconnected rational homotopy theory
Andrey Lazarev, Martin Markl
We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other…