804 research outputs found
Dwyer-Kan localization revisited
A version of Dwyer-Kan localization in the context of infinity-categories and
simplicial categories is presented. Some results of the classical papers by
Dwyer and Kan on simplicial localization are reproven and generalized. It is
proven that a Quillen pair of model categories gives rise to an adjoint pair of
the DK localizations. Also a result on localization of a family of
infinity-categories is proven. This, in particular, is applied to localization
of symmetric monoidal infinity-categories, where some (partial) results are
obtained.Comment: 24 pages, the final version, accepted to "Homology, Homotopy and
Applications
Descent of Deligne groupoids
To any non-negatively graded dg Lie algebra over a field of
characteristic zero we assign a functor from the
category of commutative local artinian -algebras with the residue field
to the category of Kan simplicial sets. There is a natural homotopy equivalence
between and the Deligne groupoid corresponding to .
The main result of the paper claims that the functor commutes up to
homotopy with the "total space" functors which assign a dg Lie algebra to a
cosimplicial dg Lie algebra and a simplicial set to a cosimplicial simplicial
set. This proves a conjecture of Schechtman which implies that if a deformation
problem is described ``locally'' by a sheaf of dg Lie algebras on a
topological space then the global deformation problem is described by the
homotopy Lie algebra .Comment: Minor corrections made AMSLaTeX v 1.2 (Compatibility mode
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