Title
Hochschild cohomology with support
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
International mathematics research notices
Volume/pages
(2015) :13 , p. 4741-4812
ISSN
1073-7928
ISI
000359714900009
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
E-info
https://repository.uantwerpen.be/docman/iruaauth/844f1b/b8e10707.pdf
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