5 citations · 7 across the 6 of their papers we have counts for
6 papers
Enhanced left triangulated categories
Xiaofa Chen
In this short note, we study dg categories with homotopy kernels, whose homotopy categories are known to admit a natural left triangulated structure. Prototypical examples of such…
Auslander--Iyama correspondence for exact dg categories
Xiaofa Chen
We extend Auslander--Iyama correspondence to the setting of exact dg categories. By specializing it to exact dg categories concentrated in degree zero, we obtain a generalization o…
On exact dg categories
Xiaofa Chen
We introduce the notion of an exact dg category, which is a simultaneous generalization of the notions of exact category in the sense of Quillen and of pretriangulated dg category…
The lower extension groups and quotient categories
Xiaofa Chen, Xiao-Wu Chen
For a certain full additive subcategory X of an additive category A, one defines the lower extension groups in relative homological algebra. We show that these groups are isomorphi…
An informal introduction to dg categories
Xiaofa Chen, Xiao-Wu Chen
In this informal introduction to dg categories, the slogan is that dg categories are more rudimentary than triangulated categories. We recall some details on the dg quotient catego…
Liftable derived equivalences and objective categories
Xiaofa Chen, Xiao-Wu Chen
We give two proofs to the following theorem and its generalization: if a finite dimensional algebra is derived equivalent to a smooth projective scheme, then any derived equiva…