Geodesic
Localizations of the Category of $A_\infty$ Categories and Internal Homs
Documenta mathematica, Tome 24 (2019), pp. 2463-2492
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital A∞​ categories with respect to the corresponding classes of quasi-equivalences are all equivalent. Moreover we show that the last two localizations are equivalent to the corresponding quotients by the relation of being isomorphic in the cohomology of the A∞​ category of A∞​ functors. As an application we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital A∞​ functors between them.
DOI : 10.4171/dm/731
Classification : 18D20, 18E35, 57T30
Mots-clés : dg categories, A∞​ categories 
@article{10_4171_dm_731,
     author = {Mattia Ornaghi and Paolo Stellari and Alberto Canonaco},
     title = {Localizations of the {Category} of $A_\infty$ {Categories} and {Internal} {Homs}},
     journal = {Documenta mathematica},
     pages = {2463--2492},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/731},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/731/}
}
TY  - JOUR
AU  - Mattia Ornaghi
AU  - Paolo Stellari
AU  - Alberto Canonaco
TI  - Localizations of the Category of $A_\infty$ Categories and Internal Homs
JO  - Documenta mathematica
PY  - 2019
SP  - 2463
EP  - 2492
VL  - 24
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/731/
DO  - 10.4171/dm/731
ID  - 10_4171_dm_731
ER  - 
%0 Journal Article
%A Mattia Ornaghi
%A Paolo Stellari
%A Alberto Canonaco
%T Localizations of the Category of $A_\infty$ Categories and Internal Homs
%J Documenta mathematica
%D 2019
%P 2463-2492
%V 24
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/731/
%R 10.4171/dm/731
%F 10_4171_dm_731
Mattia Ornaghi; Paolo Stellari; Alberto Canonaco. Localizations of the Category of $A_\infty$ Categories and Internal Homs. Documenta mathematica, Tome 24 (2019), pp. 2463-2492. doi: 10.4171/dm/731

Cité par Sources :