10 papers
Transfer of abelian model structures to equivariant categories and homotopy squares
Zhenxing Di, Liping Li, Li Liang +2
Let be a finite group acting on a Grothendieck category with enough projectives, such that is invertible in . We prove a general lifting theore…
Flat models for Q-shaped derived categories via PGF objects
Zhenxing Di, Liping Li, Li Liang +1
We develop a unified approach, based on projectively coresolved Gorenstein flat (PGF) objects, for constructing flat model structures on diagram categories. Specifically, we show t…
Standard modules and Dold-Kan correspondences for generalized Reedy categories
Liping Li
We develop a representation-theoretic approach to generalized Reedy categories through a systematic study of homomorphism spaces between standard modules. For a broad class of thes…
Representations of categories of finite relational structures and associated endomorphism monoids
Liping Li
We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For…
Representations of generalized linear Reedy categories and abelian model structures
Zhenxing Di, Liping Li, Li Liang
In this paper we consider representations of generalized -linear Reedy categories , a common generalization of -linear Reedy categories introduced by…
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories
Zhenxing Di, Liping Li, Li Liang
We prove that every Grothendieck topology induces a hereditary torsion pair in the category of presheaves of modules on a ringed site, and obtain a homological characterization of…
Constructions of Waldhausen categories via Grothendieck opfibrations
Zhenxing Di, Liping Li, Li Liang
Given a Grothendieck opfibration , we describe a method to construct a Waldhausen category structure on the total category via combini…
Compatible weak factorization systems and model structures
Zhenxing Di, Liping Li, Li Liang
In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories…
Representations of -type combinatorial categories
Zhenxing Di, Liping Li, Li Liang
In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice of partit…
Completeness of the induced cotorsion pairs in functor categories
Zhenxing Di, Liping Li, Li Liang +1
This paper focuses on a question raised by Holm and Jørgensen, who asked if the induced cotorsion pairs and in $…