1 citations · 1 across the 8 of their papers we have counts for
8 papers
Pretriangulated categories failing (TR4)
Xiao-Wu Chen, Jian Liu, Sergei O. Ivanov +3
We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category whose stable category of cohere…
The singularity category via the stabilization
Xiao-Wu Chen
We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The resu…
Noncommutative Knörrer periodicity via equivariantization
Xiao-Wu Chen, Wenchao Wu
We establish noncommutative Knörrer periodicity for projective-module factorizations over an arbitrary ring, using the equivariantization theory with respect to various actions by…
The singularity category as a stable module category
Xiao-Wu Chen, Zhengfang Wang
We investigate the stabilization of the module category over an artinian ring by formally inverting the tensor endofunctor given by the bimodule of relative nonco…
Higher-dimensional module factorizations and complete intersections
Xiao-Wu Chen
We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consistin…
Differential graded enhancements of singularity categories
Xiao-Wu Chen, Zhengfang Wang
The singularity category of a ring detects the homological singularity of the given ring, and appears in many different contexts. We describe two different dg enhancements of the s…
Pre-weight structures, pseudo-identities and canonical derived equivalences
Xiao-Wu Chen
We introduce the notion of pre-weight structure on a triangulated category and study the corresponding pseudo-identities. We propose the notion of canonical derived equivalence bet…
On extensions of covariantly finite subcategories
Xiao-Wu Chen
In \cite{GT}, Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covar…