34 citations · 260 across the 72 of their papers we have counts for
37 papers · 1 filter
Flat model structures and Gorenstein objects in functor categories
Zhenxing Di, Liping Li, Li Liang +1
We construct a flat model structure on the category of additive functors from a small preadditive category satisfying certain conditi…
Representations over diagrams of abelian categories I: Global structure and homological objects
Zhenxing Di, Liping Li, Li Liang +1
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categ…
Sheaves of modules on atomic sites and discrete representations of topological groups
Zhenxing Di, Liping Li, Li Liang +1
The main goal of this paper is to establish close relations among sheaves of modules on atomic sites, representations of categories, and discrete representations of topological gro…
Adjoint functors on the representation category of
Wee Liang Gan, Liping Li
In this paper we study adjunction relations between some natural functors on the representation category of the category of finite linearly ordered sets and order-preserving inject…
Sufficient and necessary conditions for hereditary of infinite category algebras
Malte Lackmann, Liping Li
We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally…
An inductive method for -modules
Wee Liang Gan, Liping Li
In this paper we introduce an inductive method to study -modules presented in finite degrees, where is a skeleton of the category of finitely totally ord…
Castelnuovo-Mumford regularity of representations of certain product categories
Wee Liang Gan, Liping Li
We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if t…
Classifying global dimensions of category algebras of some finite combinational categories
L. Li, T. Zhang
In this paper we classify global dimensions of the category algebras of some finite categories, including finite truncations of the categories , , , , , $…
Linear stable range for homology of congruence subgroups via FI-modules
Wee Liang Gan, Liping Li
We answer positively a question of Church, Miller, Nagpal and Reinhold on existence of a linear bound on the presentation degree of the homology of a complex of FI-modules. This im…
Local cohomology and the multi-graded regularity of FI-modules
Liping Li, Eric Ramos
We develop a local cohomology theory for FI-modules, and show that it in many ways mimics the classical theory for multi-graded modules over a polynomial ring. In particular, w…
An application of Nakayama functor in representation stability theory
Wee Liang Gan, Liping Li, Changchang Xi
Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We t…
Bounds on homological invariants of VI-modules
Wee Liang Gan, Liping Li
We give bounds for various homological invariants (including Castelnuovo-Mumford regularity, degrees of local cohomology, and injective dimension) of finitely generated VI-modules…
FI-modules over Noetherian rings
Liping Li, Nina Yu
In this paper we study representation theory of the category FI introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting repr…
Asymptotic behaviors of representations of graded categories with inductive functors
Wee Liang Gan, Liping Li
In this paper we describe an inductive machinery to investigate asymptotic behaviors of homology groups and related invariants of representations of certain graded combinatorial ca…
An inductive machinery for representations of categories with shift functors
Wee Liang Gan, Liping Li
We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P)…
Two homological proofs of the Noetherianity of
Liping Li
We give two homological proofs of the Noetherianity of the category , a fundamental result discovered by Church, Ellenberg, Farb, and Nagpal.
Depth and the Local Cohomology of FI_G-modules
Liping Li, Eric Ramos
In this paper we describe a machinery for homological calculations of representations of FI_G, and use it to develop a local cohomology theory over any commutative Noetherian ring.…
Upper bounds of homological invariants of -modules
Liping Li
In this paper we use a homological approach to obtain upper bounds for a few homological invariants of -modules . These upper bounds are expressed in terms of the generati…
Filtrations and Homological degrees of FI-modules
Liping Li, Nina Yu
Let be a commutative Noetherian ring. In this paper we consider filtered modules of the category FI firstly introduced by Nagpal. We show that a finitely generated FI-module $V…
Homological degrees of representations of categories with shift functors
Liping Li
Let be a commutative Noetherian ring and be a locally finite -linear category equipped with a self-embedding functor of degree 1. We show under a m…
On central stability
Wee Liang Gan, Liping Li
The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Churc…
Coinduction functor in representation stability theory
Wee Liang Gan, Liping Li
We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new and simpler proofs of (generalizations of) various resul…
Koszulity of directed categories in representation stability theory
Wee Liang Gan, Liping Li
In the first part of this paper, we study Koszul property of directed graded categories. In the second part of this paper, we prove a general criterion for an infinite directed cat…
Noetherian property of infinite EI categories
Wee Liang Gan, Liping Li
It is known that finitely generated FI-modules over a field of characteristic 0 are Noetherian. We generalize this result to the abstract setting of an infinite EI category satisfy…