|
Title
|
|
|
|
Hochschild cohomology with support
|
|
|
Author
|
|
|
|
|
|
|
Abstract
|
|
|
|
| In this paper, we investigate the functoriality properties of map-graded Hochschild complexes. We show that the category Map of map-graded categories is naturally a stack over the category of small categories endowed with a certain Grothendieck topology of 3-covers. For a related topology of ∞-covers on the Cartesian morphisms in Map, we prove that taking map-graded Hochschild complexes defines a sheaf. From the functoriality related to injections between map-graded categories, we obtain Hochschild complexes with support. We revisit Keller's arrow category argument from this perspective, and introduce and investigate a general Grothendieck construction which encompasses both the map-graded categories associated to presheaves of algebras and certain generalized arrow categories, which together constitute a pair of complementary tools for deconstructing Hochschild complexes. |
|
|
|
Language
|
|
|
|
English
|
|
|
Source (journal)
|
|
|
|
International mathematics research notices
|
|
|
Publication
|
|
|
|
2015
|
|
|
ISSN
|
|
|
|
1073-7928
1687-0247
|
|
|
DOI
|
|
|
|
10.1093/IMRN/RNU079
|
|
|
Volume/pages
|
|
|
|
13
(2015)
, p. 4741-4812
|
|
|
ISI
|
|
|
|
000359714900009
|
|
|
Full text (Publisher's DOI)
|
|
|
|
|
|
|
Full text (open access)
|
|
|
|
|
|
|
Full text (publisher's version - intranet only)
|
|
|
|
|
|