|
Title
|
|
|
|
On the tensor product of well generated dg categories
|
|
|
Author
|
|
|
|
|
|
|
Abstract
|
|
|
|
| We endow the homotopy category of well generated (pretriangulated) dg ca- tegories with a tensor product satisfying a universal property. The resulting monoidal structure is symmetric and closed with respect to the cocontinuous RHom of dg categories (in the sense of Toën [32]). We give a construction of the tensor product in terms of localisations of dg derived categories, making use of the enhanced derived Gabriel-Popescu theorem [27]. Given a regular cardinal 𝛼, we define and construct a tensor product of homotopically 𝛼-cocomplete dg categories and prove that the well generated tensor product of 𝛼-continuous derived dg categories (in the sense of [27]) is the 𝛼-continuous dg derived category of the homotopically 𝛼-cocomplete tensor product. In particular, this shows that the tensor product of well generated dg categories preserves 𝛼-compactness. |
|
|
|
Language
|
|
|
|
English
|
|
|
Source (journal)
|
|
|
|
Journal of pure and applied algebra. - Amsterdam
|
|
|
Publication
|
|
|
|
Amsterdam
:
2022
|
|
|
ISSN
|
|
|
|
0022-4049
|
|
|
DOI
|
|
|
|
10.1016/J.JPAA.2021.106843
|
|
|
Volume/pages
|
|
|
|
226
:3
(2022)
, 44 p.
|
|
|
Article Reference
|
|
|
|
106843
|
|
|
ISI
|
|
|
|
000704010100008
|
|
|
Medium
|
|
|
|
E-only publicatie
|
|
|
Full text (Publisher's DOI)
|
|
|
|
|
|
|
Full text (open access)
|
|
|
|
|
|
|
Full text (publisher's version - intranet only)
|
|
|
|
|
|