Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Recollements and $n$-cotorsion pairs

Weiqing Cao, Jiaqun Wei, Kaili Wu

Abstract

In the present paper, we study the relationships of $n$-cotorsion pairs among three abelian categories in a recollement. Under certain conditions, we present an explicit construction of gluing of $n$-cotorsion pairs in an abelian category $\mathcal{D}$ with respect to $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ respectively. On the other hand, we study the construction of $n$-cotorsion pairs in abelian categories $\mathcal{D}^{'}$, $\mathcal{D}^{''}$ obtained from $n$-cotorsion pairs in an abelian category $\mathcal{D}$.

Recollements and $n$-cotorsion pairs

Abstract

In the present paper, we study the relationships of -cotorsion pairs among three abelian categories in a recollement. Under certain conditions, we present an explicit construction of gluing of -cotorsion pairs in an abelian category with respect to -cotorsion pairs in abelian categories , respectively. On the other hand, we study the construction of -cotorsion pairs in abelian categories , obtained from -cotorsion pairs in an abelian category .
Paper Structure (4 sections, 16 theorems, 43 equations)

This paper contains 4 sections, 16 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. Prelimilaries
  3. $n$-Cotorsion pairs in a recollement of abelian categories
  4. Applications and examples

Key Result

Theorem 2.3

$\mathrm{{{\mathrm{HMP}}}}$ Let ${{\mathcal{A}}}$ and ${{\mathcal{B}}}$ be classes of objects in ${{\mathcal{D}}}$. Then, the following are equivalent: $(a)$$({{\mathcal{A}}},{{\mathcal{B}}})$ is a left $n$-cotorsion pair in ${{\mathcal{D}}}$; $(b)$${{\mathcal{A}}}=\bigcap_{i=1}^{n} {^{\perp_{i}}{{\

Theorems & Definitions (23)

  • Definition 2.1
  • Remark 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Definition 2.5
  • Definition 2.6
  • Lemma 2.7
  • Lemma 2.8
  • Proposition 2.9
  • Theorem 3.1
  • ...and 13 more