Categorical Realizations of Quivers

Uriya A. First

doi:10.1080/00927872.2015.1065836

Categorical Realizations of Quivers

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.

Original language	English
Pages (from-to)	2567-2582
Number of pages	16
Journal	Communications in Algebra
Volume	44
Issue number	6
DOIs	https://doi.org/10.1080/00927872.2015.1065836
State	Published - 2 Jun 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Copyright © Taylor & Francis Group, LLC.

Keywords

Additive category
Categorical realization
Fitting's lemma
Fitting's property
Pseudo-abelian category
Quiver
Semi-centralizer subring
Semi-invariant subring

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1080/00927872.2015.1065836

Cite this

@article{d49916d9ef6b4d53b22e1aafb0618909,

title = "Categorical Realizations of Quivers",

abstract = "We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.",

keywords = "Additive category, Categorical realization, Fitting's lemma, Fitting's property, Pseudo-abelian category, Quiver, Semi-centralizer subring, Semi-invariant subring",

author = "First, {Uriya A.}",

note = "Publisher Copyright: {\textcopyright} 2016, Copyright {\textcopyright} Taylor & Francis Group, LLC.",

year = "2016",

month = jun,

day = "2",

doi = "10.1080/00927872.2015.1065836",

language = "English",

volume = "44",

pages = "2567--2582",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis",

number = "6",

}

TY - JOUR

T1 - Categorical Realizations of Quivers

AU - First, Uriya A.

PY - 2016/6/2

Y1 - 2016/6/2

N2 - We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.

AB - We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.

KW - Additive category

KW - Categorical realization

KW - Fitting's lemma

KW - Fitting's property

KW - Pseudo-abelian category

KW - Quiver

KW - Semi-centralizer subring

KW - Semi-invariant subring

UR - http://www.scopus.com/inward/record.url?scp=84969915332&partnerID=8YFLogxK

U2 - 10.1080/00927872.2015.1065836

DO - 10.1080/00927872.2015.1065836

M3 - Article

AN - SCOPUS:84969915332

SN - 0092-7872

VL - 44

SP - 2567

EP - 2582

JO - Communications in Algebra

JF - Communications in Algebra

IS - 6

ER -

Categorical Realizations of Quivers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this